2. Technical Reference of the Digraph3 modules

Author:

Raymond Bisdorff, Emeritus Professor of Computer Science and Applied Mathematics

Url:

https://rbisdorff.github.io/

Version:

Python 3.11 (release: 3.11.6)

Copyright:

R. Bisdorff 2013-2023

New:

• A mpOutrankingDigraphs module for a variable start-method based multiprocessing construction of bipolar-valued outranking digraphs with main MPBipolarOutrankingDigraph class

• The digraphsTools.kmpMatch() method implements the Knuth Morris Pratt string matching algorithm

• The digraphsTools.computeSequenceAlignment() method implements the Needlemann % Wunsch dynamic programming algorithm for computing DNA sequence alignments

• A dynamicProgramming module for solving dynamic programming problems

• A pairings module for solving fair intergroup and intragroup pairing problems

Preface

It is necessary to mention that the Digraph3 Python resources do not provide a professional Python software library. The collection of Python modules was not built following any professional software development methodology. The design of classes and methods was kept as simple and elementary as was opportune for the author. Sophisticated and cryptic overloading of classes, methods and variables is more or less avoided all over. A simple copy, paste and ad hoc customisation development strategy was generally preferred. As a consequence, the Digraph3 modules keep a large part of independence.

Furthermore, the development of the Digraph3 modules being spread over two decades, the programming style did evolve with growing experience and the changes and enhancement coming up with the ongoing new releases first, of the standard Python2, and later of the standard Python3 libraries. The backward compatibility requirements necessarily introduced so with time different notation and programming techniques.

Note

Two deviating features from the usually recommended Python source coding style must be mentioned. We do not use only lowercase function names and avoid all underscore separators because of Latex editing problems. Same rule is applied to variable names, except Boolean method parameters –like Debug or Comments– where we prefer using semiotic names starting with an uppercase letter.

2.1. Installation

Dowloading the Digraph3 resources

Three download options are given:

1. Recommended: With a browser access, download and extract the latest distribution zip archive either, from

   https://github.com/rbisdorff/Digraph3 or, from

   https://sourceforge.net/projects/digraph3/

2. By using a git client and cloning either, from github.com:

   ...$ git clone https://github.com/rbisdorff/Digraph3
   

3. Or, from sourceforge.net:

   ...$ git clone https://git.code.sf.net/p/digraph3/code Digraph3
   

On Linux or Mac OS, ..$ cd to the extracted <Digraph3> directory:

../Digraph3$ make installVenv

installs the Digraph3 modules in an activated virtual Python environment (the Python recommended option), or in the user’s local python3 site-packages. As of Python 3.11, it is necessary to previously install the wheel package ( …$ python3.11 -m pip install wheel).

Whereas:

../Digraph3$ make install

installs (with sudo ${PYTHON} setup.py) the Digraph3 modules system wide in the current running python environment. Python 3.8 (or later) environment is recommended (see the makefile for adapting to your PYTHON make constant).

From Python3.10.4 on, the distutils package and the direct usage of setup.py are deprecated. The instead recommended installation via the pip module is provided with:

../Digraph3$ make installPip

This make command launches in fact a ${PYTHON} -m pip -v install –upgrade –scr = . command that installs the Digraph3 modules in the running virtual environment (recommended option) or the user’s local site-packages directory. A system wide installation is possible with prefixing the make installPip commad with sudo.

If the cython (https://cython.org/) C-compiled modules for Big Data applications are required, it is necessary to previously install the cython package and, if not yeat installed, the wheel package in the running Python environment:

...$ python3 -m pip install cython wheel

It is recommended to run a test suite:

.../Digraph3$ make tests

Test results are stored in the <Digraph3/test/results> directory. Notice that the python3 pytest package is therefore required:

...$ python3 -m pip install pytest

A verbose (with stdout not captured) pytest suite may be run as follows:

.../Digraph3$ make verboseTests

When the GNU parallel shell tool is installed and multiple processor cores are detected, the tests may be executed in multiprocessing mode:

../Digraph3$ make pTests

Individual module pytest suites are also provided (see the makefile), like the one for the outrankingDigraphs module:

../Digraph3$ make outrankingDigraphsTests

Dependencies

• To be fully functional, the Digraph3 resources mainly need the graphviz tools and the R statistics resources to be installed.

• When exploring digraph isomorphisms, the nauty isomorphism testing program is required.

2.2. Organisation of the Digraph3 modules

The Digraph3 source code is split into several interdependent modules of which the digraphs.py module is the master module.

2.2.1. Basic modules

• digraphs module

  Main part of the Digraph3 source code with the generic root Digraph class.

• graphs module

  Resources for handling undirected graphs with the generic root Graph class and a brigde to the digraphs module resources.

• perfTabs module

  Tools for handling multiple criteria performance tableaux with the generic root PerformanceTableau class.

• outrankingDigraphs module

  Root module for handling outranking digraphs with the abstract generic root OutrankingDigraph classs and the main BipolarOutrankingDigraph class. Notice that the outrankingDigraph class defines a hybrid object type, inheriting conjointly from the Digraph class and the PerformanceTableau class.

• votingProfiles module

  Classes and methods for handling voting ballots and computing election results with main LinearVotingProfile class.

• pairings module

  Classes and methods for computing fair pairings solutions with abstract generic root Pairing class.

• dynamicProgramming module

  Classes and methods for solving dynamic programming problems with generic root DynamicProgrammingDigraph class.

2.2.2. Various Random generators

• randomDigraphs module

  Various implemented random digraph models.

• randomPerfTabs module

  Various implemented random performance tableau models.

• randomNumbers module

  Additional random number generators, not available in the standard python random.py library.

2.2.3. Handling big data

• performanceQuantiles module

  Incremental representation of large performance tableaux via binned cumulated density functions per criteria. Depends on the randomPerfTabs module.

• sparseOutrankingDigraphs module

  Sparse implementation design for large bipolar outranking digraphs (order > 1000);

• mpOutrankingDigraphs module

  New variable start-methods based multiprocessing construction of genuine bipolar-valued outranking digraphs.

2.2.4. Cythonized modules

• Cythonized modules for big digraphs

  Cythonized C implementation for handling big performance tableaux and bipolar outranking digraphs (order > 1000).

2.2.5. Sorting, rating and ranking tools

• ratingDigraphs module

  Tools for solving relative and absolute rating problems with the abstract generic root RatingDigraph class;

• sortingDigraphs module

  Additional tools for solving sorting problems with the generic root SortingDigraph class and the main QuantilesSortingDigraph class;

• linearOrders module

  Additional tools for solving linearly ranking problems with the abstract generic root LinearOrder class;

• transitiveDigraphs module

  Additional tools for solving pre-ranking problems with abstract generic root TransitiveDigraph class.

2.2.6. Miscellaneous tools

• digraphsTools module

  Various generic methods and tools for handling digraphs.

• arithmetics module

  Some common methods and tools for computing with integer numbers.

---

2.3. digraphs module

A tutorial with coding examples is available here: Working with the Digraph3 software resources

Inheritance Diagram

Python3+ implementation of the digraphs module, root module of the Digraph3 resources.

Copyright (C) 2006-2023 Raymond Bisdorff

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

class digraphs.AsymmetricPartialDigraph(digraph)

Renders the asymmetric part of a Digraph instance.

Note

• The non asymmetric and the reflexive links are all put to the median indeterminate characteristic value!

• The constructor makes a deep copy of the given Digraph instance!

class digraphs.BipartitePartialDigraph(digraph, partA, partB, Partial=True)

Renders the bipartite part of a Digraph instance.

Note

• partA and partB must be parts of the actions attribute of the given Digraph instance

• The non-bipartite links are all put to the median indeterminate characteristic value

• The constructor makes a deep copy of the given Digraph instance

class digraphs.BreakAddCocsDigraph(digraph=None, Cpp=False, Piping=False, Comments=False, Threading=False, nbrOfCPUs=1)

Specialization of general Digraph class for instantiation of chordless odd circuits augmented digraphs.

Parameters:

• digraph: Stored or memory resident digraph instance.

• Cpp: using a C++/Agrum version of the Digraph.computeChordlessCircuits() method.

• Piping: using OS pipes for data in- and output between Python and C++.

A chordless odd circuit is added if the cumulated credibility of the circuit supporting arcs is larger or equal to the cumulated credibility of the converse arcs. Otherwise, the circuit is broken at the weakest asymmetric link, i.e. a link (x, y) with minimal difference between r(x S y) - r(y S x).

addCircuits(Comments=False)

Augmenting self with self.circuits.

closureChordlessOddCircuits(Cpp=False, Piping=False, Comments=True, Debug=False, Threading=False, nbrOfCPUs=1)

Closure of chordless odd circuits extraction.

showCircuits(credibility=None, Debug=False)

show methods for chordless odd circuits in CocaGraph

showComponents()

Shows the list of connected components of the digraph instance.

class digraphs.BrokenChordlessCircuitsDigraph(digraph=None, Cpp=False, Piping=False, Comments=False, Threading=False, nbrOfCPUs=1)

Specialization of general Digraph class for instantiation of chordless circuits broken digraphs.

Parameters:

• digraph: stored or memory resident digraph instance.

• Cpp: using a C++/Agrum version of the Digraph.computeChordlessCircuits() method.

• Piping: using OS pipes for data in- and output between Python and C++.

All chordless odd circuits are broken at the weakest asymmetric link, i.e. a link with minimal difference between and .

breakChordlessOddCircuits(Cpp=False, Piping=False, Comments=True, Debug=False, Threading=False, nbrOfCPUs=1)

Breaking of chordless odd circuits extraction.

breakCircuits(Comments=False)

Break all cricuits in self.circuits.

showComponents()

Shows the list of connected components of the digraph instance.

class digraphs.BrokenCocsDigraph(digraph=None, Cpp=False, Piping=False, Comments=False, Threading=False, nbrOfCPUs=1)

Specialization of general Digraph class for instantiation of chordless odd circuits broken digraphs.

Parameters:

• digraph: stored or memory resident digraph instance.

• Cpp: using a C++/Agrum version of the Digraph.computeChordlessCircuits() method.

• Piping: using OS pipes for data in- and output between Python and C++.

All chordless odd circuits are broken at the weakest asymmetric link, i.e. a link with minimal difference between and .

breakChordlessOddCircuits(Cpp=False, Piping=False, Comments=True, Debug=False, Threading=False, nbrOfCPUs=1)

Breaking of chordless odd circuits extraction.

breakCircuits(Comments=False)

Break all cricuits in self.circuits.

showComponents()

Shows the list of connected components of the digraph instance.

class digraphs.CSVDigraph(fileName='temp', valuationMin=-1, valuationMax=1)

Specialization of the general Digraph class for reading stored csv formatted digraphs. Using the inbuilt module csv.

Param:

fileName (without the extension .csv).

showAll()

Detailed show method for genuine digraphs.

class digraphs.CirculantDigraph(order=7, valuationdomain={'max': Decimal('1.0'), 'min': Decimal('-1.0')}, circulants=[-1, 1], IndeterminateInnerPart=False)

Specialization of the general Digraph class for generating temporary circulant digraphs.

Parameters:

order > 0;

valuationdomain ={‘min’:m, ‘max’:M};

circulant connections = list of positive and/or negative circular shifts of value 1 to n.

Default instantiation C_7:

order = 7,

valuationdomain = {‘min’:-1.0,’max’:1.0},

circulants = [-1,1].

Example session:

>>> from digraphs import CirculantDigraph
>>> c8 = CirculantDigraph(order=8,circulants=[1,3])
>>> c8.exportGraphViz('c8')
*---- exporting a dot file for GraphViz tools ---------*
Exporting to c8.dot
circo -Tpng c8.dot -o c8.png
# see below the graphviz drawing
>>> c8.showChordlessCircuits()
No circuits yet computed. Run computeChordlessCircuits()!
>>> c8.computeChordlessCircuits()
...
>>> c8.showChordlessCircuits()
*---- Chordless circuits ----*
['1', '4', '7', '8'] , credibility : 1.0
['1', '4', '5', '6'] , credibility : 1.0
['1', '4', '5', '8'] , credibility : 1.0
['1', '2', '3', '6'] , credibility : 1.0
['1', '2', '5', '6'] , credibility : 1.0
['1', '2', '5', '8'] , credibility : 1.0
['2', '3', '6', '7'] , credibility : 1.0
['2', '3', '4', '7'] , credibility : 1.0
['2', '5', '6', '7'] , credibility : 1.0
['3', '6', '7', '8'] , credibility : 1.0
['3', '4', '7', '8'] , credibility : 1.0
['3', '4', '5', '8'] , credibility : 1.0
12 circuits.
>>>

showShort()

concise presentation method for genuine digraphs.

class digraphs.CoDualDigraph(other, Debug=False)

Instantiates the associated codual -converse of the negation- from a deep copy of a given Digraph instance called other.

Note

Instantiates self as other.__class__ ! And, deepcopies, the case given, the other.description, the other.criteria and the other.evaluation dictionaries into self.

class digraphs.CocaDigraph(digraph=None, Cpp=False, Piping=False, Comments=False)

Old CocaDigraph class without circuit breakings; all circuits and circuits of circuits are added as hyper-nodes.

Warning

May sometimes give inconsistent results when an autranking digraph shows loads of chordless cuircuits. It is recommended in this case to use instead either the BrokenCocsDigraph class (preferred option) or the BreakAddCocsDigraph class.

Parameters:

• digraph: Stored or memory resident digraph instance.

• Cpp: using a C++/Agrum version of the Digraph.computeChordlessCircuits() method.

• Piping: using OS pipes for data in- and output between Python and C++.

Specialization of general Digraph class for instantiation of chordless odd circuits augmented digraphs.

addCircuits(Comments=False)

Augmenting self with self.circuits.

closureChordlessOddCircuits(Cpp=False, Piping=False, Comments=False)

Closure of chordless odd circuits extraction.

showCircuits(credibility=None)

show methods for chordless odd circuits in CocaGraph

showComponents()

Shows the list of connected components of the digraph instance.

class digraphs.CompleteDigraph(order=5, valuationdomain=(-1.0, 1.0))

Specialization of the general Digraph class for generating temporary complete graphs of order 5 in {-1,0,1} by default.

Parameters:

order > 0; valuationdomain=(Min,Max).

class digraphs.ConverseDigraph(other)

Instantiates the associated converse or reciprocal version from a deep copy of a given Digraph called other.

Instantiates as other.__class__ !

Deep copies, the case given, the description, the criteria and the evaluation dictionaries into self.

class digraphs.CoverDigraph(other, Debug=False)

Instantiates the associated cover relation -immediate neighbours- from a deep copy of a given Digraph called other. The Hasse diagram for instance is the cover relation of a transitive digraph.

Note

Instantiates as other.__class__ ! Copies the case given the other.description, the other.criteria and the other.evaluation dictionaries into self.

class digraphs.CriteriaCorrelationDigraph(outrankingDigraph, ValuedCorrelation=True, WithMedian=False)

Renders the ordinal criteria correlation digraph from the given outranking digraph.

If ValuedCorrelation==True, the correlation indexes represent the bipolar-valued p airwise relational equivalence between the marginal criteria outranking relation: that is tau * determination

Otherwise, the valuation represents the ordinal correlation index tau

If WithMedian==True, the correlation of the marginal criteria outranking with the global outranking relation, denoted ‘m’, is included.

exportPrincipalImage(plotFileName=None, pictureFormat='pdf', bgcolor='cornsilk', fontcolor='red3', fontsize='0.85', tempDir='.', Comments=False)

Export the principal projection of the absolute correlation distances using the three principal eigen vectors.

Implemeted picture formats are: ‘pdf’ (default), ‘png’, ‘jpeg’ and ‘xfig’.

The background, resp. font color is set by default to ‘cornsilk’, resp. ‘red3’.

_Colwise and _Reduced parameters are deprecated.

Warning

The method, writing and reading temporary files: tempCol.r and rotationCol.csv, resp. tempRow.r and rotationRow.csv, by default in the working directory (./), is hence not safe for multiprocessing programs, unless a temporary directory tempDir is provided.

class digraphs.Digraph(file=None, order=7)

Genuine root class of all Digraph3 modules. See Digraph3 tutorials.

All instances of the digraphs.Digraph class contain at least the following components:

1. A collection of digraph nodes called actions (decision alternatives): a list, set or (ordered) dictionary of nodes with ‘name’ and ‘shortname’ attributes,

2. A logical characteristic valuationdomain, a dictionary with three decimal entries: the minimum (-1.0, means certainly false), the median (0.0, means missing information) and the maximum characteristic value (+1.0, means certainly true),

3. The digraph relation : a double dictionary indexed by an oriented pair of actions (nodes) and carrying a characteristic value in the range of the previous valuation domain,

4. Its associated gamma function : a dictionary containing the direct successors, respectively predecessors of each action, automatically added by the object constructor,

5. Its associated notGamma function : a dictionary containing the actions that are not direct successors respectively predecessors of each action, automatically added by the object constructor.

A previously stored digraphs.Digraph instance may be reloaded with the file argument:

>>> from randomDigraphs import RandomValuationDigraph
>>> dg = RandomValuationDigraph(order=3,Normalized=True,seed=1)
>>> dg.save('testdigraph')
Saving digraph in file: <testdigraph.py> 
>>> from digraphs import Digraph
>>> dg = Digraph(file='testdigraph') # without the .py extenseion
>>> dg.__dict__
{'name': 'testdigraph',
'actions': {'a1': {'name': 'random decision action', 'shortName': 'a1'},
            'a2': {'name': 'random decision action', 'shortName': 'a2'},
            'a3': {'name': 'random decision action', 'shortName': 'a3'}},
'valuationdomain': {'min': Decimal('-1.0'), 'med': Decimal('0.0'),
                        'max': Decimal('1.0'), 'hasIntegerValuation': False,},
'relation': {'a1': {'a1': Decimal('0.0'), 'a2': Decimal('-0.66'), 'a3': Decimal('0.44')},
             'a2': {'a1': Decimal('0.94'), 'a2': Decimal('0.0'), 'a3': Decimal('-0.84')},
             'a3': {'a1': Decimal('-0.36'), 'a2': Decimal('-0.70'), 'a3': Decimal('0.0')}},
'order': 3,
'gamma': {'a1': ({'a3'}, {'a2'}), 'a2': ({'a1'}, set()), 'a3': (set(), {'a1'})},
'notGamma': {'a1': ({'a2'}, {'a3'}),
             'a2': ({'a3'}, {'a1', 'a3'}),
             'a3': ({'a1', 'a2'}, {'a2'})}}
>>>

MISgen(S, I)

generator of maximal independent choices (voir Byskov 2004):

• S ::= remaining nodes;

• I ::= current independent choice

Note

Inititalize: self.MISgen(self.actions.copy(),set())

absirred(choice)

Renders the crips -irredundance degree of a choice.

absirredundant(U)

Generates all -irredundant choices of a digraph.

absirredval(choice, relation)

Renders the valued -irredundance degree of a choice.

absirredx(choice, x)

Computes the crips -irredundance degree of node x in a choice.

abskernelrestrict(prekernel)

Parameter: prekernel Renders absorbent prekernel restricted relation.

absorb(choice)

Renders the absorbency degree of a choice.

absorbentChoices(S)

Generates all minimal absorbent choices of a bipolar valued digraph.

agglomerationDistribution()

Output: aggloCoeffDistribution, meanCoeff Renders the distribution of agglomeration coefficients.

aneighbors(node)

Renders the set of absorbed in-neighbors of a node.

automorphismGenerators()

Adds automorphism group generators to the digraph instance.

Note

Dependency: Uses the dreadnaut command from the nauty software package. See https://www3.cs.stonybrook.edu/~algorith/implement/nauty/implement.shtml

On Ubuntu Linux:

…$ sudo apt-get install nauty

averageCoveringIndex(choice, direction='out')

Renders the average covering index of a given choice in a set of objects, ie the average number of choice members that cover each non selected object.

bipolarKCorrelation(digraph, Debug=False)

Renders the bipolar Kendall correlation between two bipolar valued digraphs computed from the average valuation of the XORDigraph(self,digraph) instance.

Warning

Obsolete! Is replaced by the self.computeBipolarCorrelation(other) Digraph method

bipolarKDistance(digraph, Debug=False)

Renders the bipolar crisp Kendall distance between two bipolar valued digraphs.

Warning

Obsolete! Is replaced by the self.computeBipolarCorrelation(other, MedianCut=True) Digraph method

chordlessPaths(Pk, n2, Odd=False, Comments=False, Debug=False)

New procedure from Agrum study April 2009 recursive chordless path extraction starting from path Pk = [n2, …., n1] and ending in node n2. Optimized with marking of visited chordless P1s.

circuitAverageCredibility(circ)

Renders the average linking credibility of a Chordless Circuit.

circuitCredibilities(circuit, Debug=False)

Renders the average linking credibilities and the minimal link of a Chordless Circuit.

circuitMaxCredibility(circ)

Renders the maximal linking credibility of a Chordless Circuit.

circuitMinCredibility(circ)

Renders the minimal linking credibility of a Chordless Circuit.

closeSymmetric(InSite=True)

Produces the symmetric closure of self.relation.

closeTransitive(Reverse=False, InSite=True, Comments=False)

Produces the transitive closure of self.relation.

Parameters:

• If Reverse == True (False default) all transitive links are dropped, otherwise all transitive links are closed with min[r(x,y),r(y,z)];

• If Insite == False (True by default) the methods return a modified copy of self.relation without altering the original self.relation, otherwise self.relation is modified.

components()

Renders the list of connected components.

computeAllDensities(choice=None)

parameter: choice in self renders six densitiy parameters: arc density, double arc density, single arc density, strict single arc density, absence arc density, strict absence arc densitiy.

computeArrowRaynaudOrder()

Renders a linear ordering from worst to best of the actions following Arrow&Raynaud’s rule.

computeArrowRaynaudRanking()

renders a linear ranking from best to worst of the actions following Arrow&Raynaud’s rule.

computeAverageValuation()

Computes the bipolar average correlation between self and the crisp complete digraph of same order of the irreflexive and determined arcs of the digraph

computeBadChoices(Comments=False)

Computes characteristic values for potentially bad choices.

Note

Returns a tuple with following content:

[(0)-determ,(1)degirred,(2)degi,(3)degd,(4)dega,(5)str(choice),(6)absvec]

computeBadPirlotChoices(Comments=False)

Characteristic values for potentially bad choices using the Pirlot’s fixpoint algorithm.

computeBestChoiceRecommendation(Verbose=False, Comments=False, ChoiceVector=False, CoDual=True, Debug=False, _OldCoca=False, BrokenCocs=True, Cpp=False)

Sets self.bestChoice, self.bestChoiceData, self.worstChoice and self.worstChoiceData with the showBestChoiceRecommendation method.

First and last choices data is the following: [(0)-determ,(1)degirred,(2)degi,(3)degd,(4)dega,(5)str(choice),(6)domvec,(7)cover]

self.bestChoice = self.bestChoiceData[5] self.worstChoice = self.worstChoiceData[5]

computeBipolarCorrelation(other, MedianCut=False, filterRelation=None, Debug=False)

obsolete: dummy replacement for Digraph.computeOrdinalCorrelation method

computeChordlessCircuits(Odd=False, Comments=False, Debug=False)

Renders the set of all chordless circuits detected in a digraph. Result is stored in <self.circuitsList> holding a possibly empty list of tuples with at position 0 the list of adjacent actions of the circuit and at position 1 the set of actions in the stored circuit.

When Odd is True, only chordless circuits with an odd length are collected.

computeChordlessCircuitsMP(Odd=False, Threading=False, nbrOfCPUs=None, Comments=False, Debug=False)

Multiprocessing version of computeChordlessCircuits().

Renders the set of all chordless odd circuits detected in a digraph. Result (possible empty list) stored in <self.circuitsList> holding a possibly empty list tuples with at position 0 the list of adjacent actions of the circuit and at position 1 the set of actions in the stored circuit. Inspired by Dias, Castonguay, Longo, Jradi, Algorithmica (2015).

Returns a possibly empty list of tuples (circuit,frozenset(circuit)).

If Odd == True, only circuits of odd length are retained in the result.

computeCoSize()

Renders the number of non validated non reflexive arcs

computeConcentrationIndex(X, N)

Renders the Gini concentration index of the X serie. N contains the partial frequencies. Based on the triangle summation formula.

computeConcentrationIndexTrapez(X, N)

Renders the Gini concentration index of the X serie. N contains the partial frequencies. Based on the triangles summation formula.

computeCondorcetLosers()

Wrapper for condorcetLosers().

computeCondorcetWinners()

Wrapper for condorcetWinners().

computeCopelandOrder()

renders a linear ordering from worst to best of the actions following Arrow&Raynaud’s rule.

computeCopelandRanking()

renders a linear ranking from best to worst of the actions following Arrow&Raynaud’s rule.

computeCppChordlessCircuits(Odd=False, Debug=False)

python wrapper for the C++/Agrum based chordless circuits enumeration exchange arguments with external temporary files

Result in self.circuitsList.

Warning

Deprecated !!! The python vesion is more efficient

computeCppInOutPipingChordlessCircuits(Odd=False, Debug=False)

python wrapper for the C++/Agrum based chordless circuits enumeration exchange arguments with external temporary files

Result in self.circuitsList.

Warning

Deprecated !!! The python vesion is more efficient

computeCutLevelDensities(choice, level)

parameter: choice in self, robustness level renders three robust densitiy parameters: robust double arc density, robust single arc density, robust absence arc densitiy.

computeDensities(choice)

parameter: choice in self renders the four densitiy parameters: arc density, double arc density, single arc density, absence arc density.

computeDeterminateness(InPercents=False)

Computes the Kendalll distance of self with the all median-valued indeterminate digraph of order n.

Return the average determination of the irreflexive part of the digraph.

determination = sum_(x,y) { abs[ r(xRy) - Med ] } / n(n-1)

If InPercents is True, returns the average determination in percentage of (Max - Med) difference.

>>> from outrankingDigraphs import BipolarOutrankingDigraph
>>> from randomPerfTabs import Random3ObjectivesPerformanceTableau
>>> t = Random3ObjectivesPerformanceTableau(numberOfActions=7,numberOfCriteria=7,seed=101)
>>> g = BipolarOutrankingDigraph(t,Normalized=True)
>>> g
*------- Object instance description ------*
Instance class      : BipolarOutrankingDigraph
Instance name       : rel_random3ObjectivesPerfTab
Actions             : 7
Criteria            : 7
Size                : 27
Determinateness (%) : 65.67
Valuation domain    : [-1.00;1.00]
>>> print(g.computeDeterminateness())
0.3134920634920634920634920638
>>> print(g.computeDeterminateness(InPercents=True))
65.67460317460317460317460320
>>> g.recodeValuation(0,1)
>>> g
*------- Object instance description ------*
Instance class      : BipolarOutrankingDigraph
Instance name       : rel_random3ObjectivesPerfTab
Actions             : 7
Criteria            : 7
Size                : 27
Determinateness (%) : 65.67
Valuation domain    : [0.00;1.00]
>>> print(g.computeDeterminateness())
0.1567460317460317460317460318
>>> print(g.computeDeterminateness(InPercents=True))
65.67460317460317460317460320

computeDiameter(Oriented=True)

Renders the (by default oriented) diameter of the digraph instance

computeDigraphCentres(WeakDistances=False, Comments=False)

The centers of a digraph are the nodes with finite minimal shortes path lengths.

The maximal neighborhood distances are stored in self.maximalNeighborhoodDistances.

The corresponding digraph radius and diameter are stored respectively in self.radius and self.diameter.

With Comments = True, all these results are printed out.

Source: Claude Berge, The Theory of Graphs, Dover (2001) pp. 119, original in French Dunod (1958)

computeDynamicProgrammingStages(source, sink, Debug=False)

Renders the discrete stages of the optimal substructure for dynamic pogramming digrahs from a given source node to a given sink sink node.

Returns a list of list of action identifyers.

computeGoodChoiceVector(ker, Comments=False)

Computing Characteristic values for dominant pre-kernels

using the von Neumann dual fixoint equation

computeGoodChoices(Comments=False)

Computes characteristic values for potentially good choices.

..note:

Return a tuple with following content:

[(0)-determ,(1)degirred,(2)degi,(3)degd,(4)dega,(5)str(choice),(6)domvec,(7)cover]

computeGoodPirlotChoices(Comments=False)

Characteristic values for potentially good choices using the Pirlot fixpoint algorithm.

computeIncomparabilityDegree(InPercents=False, Comments=False)

Renders the incomparability degree (Decimal), i.e. the relative number of symmetric indeterminate relations of the irreflexive part of a digraph.

computeKemenyIndex(otherRelation)

renders the Kemeny index of the self.relation compared with a given crisp valued relation of a compatible other digraph (same nodes or actions).

computeKemenyOrder(orderLimit=7, Debug=False)

Renders a ordering from worst to best of the actions with maximal Kemeny index. Return a tuple: kemenyOrder (from worst to best), kemenyIndex

computeKemenyRanking(orderLimit=7, seed=None, sampleSize=1000, Debug=False)

Renders a ranking from best to worst of the actions with maximal Kemeny index.

Note

Returns a tuple: kemenyRanking (from best to worst), kemenyIndex.

computeKernelVector(kernel, Initial=True, Comments=False)

Computing Characteristic values for dominant pre-kernels

using the von Neumann dual fixpoint equation

computeKohlerOrder()

Renders an ordering (worst to best) of the actions following Kohler’s rule.

computeKohlerRanking()

Renders a ranking (best to worst) of the actions following Kohler’s rule.

computeMaxHoleSize(Comments=False)

Renders the length of the largest chordless cycle in the corresponding disjunctive undirected graph.

computeMeanInDegree()

Renders the mean indegree of self. !!! self.size must be set previously !!!

computeMeanOutDegree()

Renders the mean degree of self. !!! self.size must be set previously !!!

computeMeanSymDegree()

Renders the mean degree of self. !!! self.size must be set previously !!!

computeMedianOutDegree()

Renders the median outdegree of self. !!! self.size must be set previously !!!

computeMedianSymDegree()

Renders the median symmetric degree of self. !!! self.size must be set previously !!!

computeMoreOrLessUnrelatedPairs()

Renders a list of more or less unrelated pairs.

computeNetFlowsOrder()

Renders an ordered list (from worst to best) of the actions following the net flows ranking rule.

computeNetFlowsRanking()

Renders an ordered list (from best to worst) of the actions following the net flows ranking rule.

computeODistance(op2, comments=False)

renders the squared normalized distance of two digraph valuations.

Note

op2 = digraphs of same order as self.

computeOrbit(choice, withListing=False)

renders the set of isomorph copies of a choice following the automorphism of the digraph self

computeOrderCorrelation(order, Debug=False)

Renders the ordinal correlation K of a digraph instance when compared with a given linear order (from worst to best) of its actions

K = sum_{x != y} [ min( max(-self.relation(x,y)),other.relation(x,y), max(self.relation(x,y),-other.relation(x,y)) ]

K /= sum_{x!=y} [ min(abs(self.relation(x,y),abs(other.relation(x,y)) ]

Note

Renders a dictionary with the key ‘correlation’ containing the actual bipolar correlation index and the key ‘determination’ containing the minimal determination level D of self and the other relation.

D = sum_{x != y} min(abs(self.relation(x,y)),abs(other.relation(x,y)) / n(n-1)

where n is the number of actions considered.

The correlation index with a completely indeterminate relation is by convention 0.0 at determination level 0.0 .

Warning

self must be a normalized outranking digraph instance !

computeOrdinalCorrelation(other, MedianCut=False, filterRelation=None, Debug=False)

Renders the bipolar correlation K of a self.relation when compared with a given compatible (same actions set)) digraph or a [-1,1] valued compatible relation (same actions set).

If MedianCut=True, the correlation is computed on the median polarized relations.

If filterRelation is not None, the correlation is computed on the partial domain corresponding to the determined part of the filter relation.

Warning

Notice that the ‘other’ relation and/or the ‘filterRelation’, the case given, must both be normalized, ie [-1,1]-valued !

K = sum_{x != y} [ min( max(-self.relation[x][y]),other.relation[x][y]), max(self.relation[x][y],-other.relation[x][y]) ]

K /= sum_{x!=y} [ min(abs(self.relation[x][y]),abs(other.relation[x][y])) ]

Note

Renders a tuple with at position 0 the actual bipolar correlation index and in position 1 the minimal determination level D of self and the other relation.

D = sum_{x != y} min(abs(self.relation[x][y]),abs(other.relation[x][y])) / n(n-1)

where n is the number of actions considered.

The correlation index with a completely indeterminate relation is by convention 0.0 at determination level 0.0 .

computeOrdinalCorrelationMP(other, MedianCut=False, Threading=True, nbrOfCPUs=None, Comments=False, Debug=False)

Multi processing version of the digraphs.computeOrdinalCorrelation() method.

Note

The relation filtering and the MedinaCut option are not implemented in the MP version.

computePairwiseClusterComparison(K1, K2, Debug=False)

Computes the pairwise cluster comparison credibility vector from bipolar-valued digraph g. with K1 and K2 disjoint lists of action keys from g actions disctionary. Returns the dictionary {‘I’: Decimal(),’P+’:Decimal(),’P-‘:Decimal(),’R’ :Decimal()} where one and only one item is strictly positive.

computePreKernels()

computing dominant and absorbent preKernels:

Result in self.dompreKernels and self.abspreKernels

computePreRankingRelation(preRanking, Normalized=True, Debug=False)

Renders the bipolar-valued relation obtained from a given preRanking in decreasing levels (list of lists) result.

computePreorderRelation(preorder, Normalized=True, Debug=False)

Renders the bipolar-valued relation obtained from a given preordering in increasing levels (list of lists) result.

computePrincipalOrder(Colwise=False, Comments=False)

Rendesr an ordering from wrost to best of the decision actions.

computePrincipalRanking(Colwise=False, Comments=False)

Rendesr a ranking from best to worst of the decision actions.

computePrincipalScores(plotFileName=None, Colwise=False, imageType=None, tempDir=None, bgcolor='cornsilk', Comments=False, Debug=False)

Renders a ordered list of the first principal eigenvector of the covariance of the valued outdegrees of self.

Note

The method, relying on writing and reading temporary files by default in a temporary directory is threading and multiprocessing safe ! (see Digraph.exportPrincipalImage method)

computePrudentBetaLevel(Debug=False)

computes alpha, ie the lowest valuation level, for which the bipolarly polarised digraph doesn’t contain a chordless circuit.

computeRankingByBestChoosing(CoDual=False, CppAgrum=False, Debug=False)

Computes a weak preordering of the self.actions by recursive best choice elagations.

Stores in self.rankingByBestChoosing[‘result’] a list of (P+,bestChoice) tuples where P+ gives the best choice complement outranking average valuation via the computePairwiseClusterComparison method.

If self.rankingByBestChoosing[‘CoDual’] is True, the ranking-by-choosing was computed on the codual of self.

computeRankingByBestChoosingRelation(rankingByBestChoosing=None, Debug=False)

Renders the bipolar-valued relation obtained from the self.rankingByBestChoosing result.

computeRankingByChoosing(actionsSubset=None, CppAgrum=False, Debug=False, CoDual=False)

Computes a weak preordring of the self.actions by iterating jointly first and last choice elagations.

Stores in self.rankingByChoosing[‘result’] a list of ((P+,bestChoice),(P-,worstChoice)) pairs where P+ (resp. P-) gives the best (resp. worst) choice complement outranking (resp. outranked) average valuation via the computePairwiseClusterComparison method.

If self.rankingByChoosing[‘CoDual’] is True, the ranking-by-choosing was computed on the codual of self.

computeRankingByChoosingRelation(rankingByChoosing=None, actionsSubset=None, Debug=False)

Renders the bipolar-valued relation obtained from the self.rankingByChoosing result.

computeRankingByLastChoosing(CoDual=False, CppAgrum=False, Debug=False)

Computes a weak preordring of the self.actions by iterating worst choice elagations.

Stores in self.rankingByLastChoosing[‘result’] a list of (P-,worstChoice) pairs where P- gives the worst choice complement outranked average valuation via the computePairwiseClusterComparison method.

If self.rankingByChoosing[‘CoDual’] is True, the ranking-by-last-chossing was computed on the codual of self.

computeRankingByLastChoosingRelation(rankingByLastChoosing=None, Debug=False)

Renders the bipolar-valued relation obtained from the self.rankingByLastChoosing result.

computeRankingCorrelation(ranking, Debug=False)

Renders the ordinal correlation K of a digraph instance when compared with a given linear ranking of its actions

K = sum_{x != y} [ min( max(-self.relation(x,y)),other.relation(x,y), max(self.relation(x,y),-other.relation(x,y)) ]

K /= sum_{x!=y} [ min(abs(self.relation(x,y),abs(other.relation(x,y)) ]

Note

Renders a tuple with at position 0 the actual bipolar correlation index and in position 1 the minimal determination level D of self and the other relation.

D = sum_{x != y} min(abs(self.relation(x,y)),abs(other.relation(x,y)) / n(n-1)

where n is the number of actions considered.

The correlation index with a completely indeterminate relation is by convention 0.0 at determination level 0.0 .

computeRelationalStructure(Debug=False)

Renders the counted decomposition of the valued relations into the following type of links: gt ‘>’, eq ‘=’, lt ‘<’, incomp ‘<>’, leq ‘<=’, geq ‘>=’, indeterm ‘?’

computeRubisChoice(CppAgrum=False, Comments=False, _OldCoca=False, BrokenCocs=True, Threading=False, nbrOfCPUs=1)

Renders self.strictGoodChoices, self.nullChoices self.strictBadChoices, self.nonRobustChoices.

CppgArum = False (default | true : use C++/Agrum digraph library for computing chordless circuits in self.

Warning

Changes in site the outranking digraph by adding or braking chordless odd outranking circuits.

computeRubyChoice(CppAgrum=False, Comments=False, _OldCoca=False)

dummy for computeRubisChoice() old versions compatibility.

computeShortestPathLengths(WeakPaths=False, Comments=False, Debug=False)

Renders a double dictionary with the directed distances, i.e. the shortest path lengths between all self.actions.

Equals None if there does not exist a directed path between two actions.

Source: Claude Berge, The Theory of Graphs, Dover (2001) pp. 119, original in French Dunod (1958)

computeSingletonRanking(Comments=False, Debug=False)

Renders the sorted bipolar net determinatation of outrankingness minus outrankedness credibilities of all singleton choices.

res = ((netdet,singleton,dom,absorb)+)

computeSize()

Renders the number of validated non reflexive arcs

computeSizeTransitiveClosure()

Renders the size of the transitive closure of a digraph.

computeSlaterOrder(isProbabilistic=False, seed=None, sampleSize=1000, Debug=False)

Reversed return from computeSlaterRanking method.

computeSlaterRanking(isProbabilistic=False, seed=None, sampleSize=1000, Debug=False)

Renders a ranking of the actions with minimal Slater index. Return a tuple: slaterOrder, slaterIndex

computeSymmetryDegree(InPercents=False, Comments=False)

Renders the symmetry degree (Decimal) of the irreflexive part of a digraph.

Note

Empty and indeterminate digraphs are considered to be symmetric.

computeTopologicalRanking(Debug=False)

Mimetic Wrapper of the topologicalSort() method.

computeTransitivityDegree(InPercents=False, Comments=False)

Renders the transitivity degree (Decimal) of a digraph.

Note

An empty or indeterminate digraph is considered to be transitive.

computeUnrelatedPairs()

Renders a list of more or less unrelated pairs.

computeValuationLevels(choice=None, Debug=False)

renders the symmetric closure of the apparent valuations levels of self in an increasingly ordered list. If parameter choice is given, the computation is limited to the actions of the choice.

computeValuationPercentages(choice, percentiles, withValues=False)

Parameters: choice and list of percentiles. renders a series of percentages of the characteristics valuation of the arcs in the digraph.

computeValuationPercentiles(choice, percentages, withValues=False)

Parameters: choice and list of percentages. renders a series of quantiles of the characteristics valuation of the arcs in the digraph.

computeValuationStatistics(Sampling=False, Comments=False)

Renders the mean and variance of the valuation of the non reflexive pairs.

computeValuedRankingRelation(ranking)

Renders the valued relation characteristics compatible with the given linar ranking. Discordant charcateristics are set to the indeterminate value.

computeWeakCondorcetLosers()

Wrapper for weakCondorcetLosers().

computeWeakCondorcetWinners()

Wrapper for weakCondorcetWinners().

computeupdown1(s, S)

Help method for show_MIS_HB2 method. fills self.newmisset, self.upmis, self.downmis.

computeupdown2(s, S)

Help method for show_MIS_HB1 method. Fills self.newmisset, self.upmis, self.downmis.

computeupdown2irred(s, S)

Help method for show_MIS_HB1 method. Fills self.newmisset, self.upmis, self.downmis.

condorcetLosers()

Renders the set of decision actions x such that self.relation[x][y] < self.valuationdomain[‘med’] for all y != x.

condorcetWinners()

Renders the set of decision actions x such that self.relation[x][y] > self.valuationdomain[‘med’] for all y != x.

contra(v)

Parameter: choice. Renders the negation of a choice v characteristic’s vector.

convertRelationToDecimal()

Converts the float valued self.relation in a decimal valued one.

convertValuation2Integer(InSite=True, Comments=False)

Converts the self.relation valuation to integer values by converting the Decimals to Fractions and multiply by the least commun multiple of the fraction denominators.

Parameters:

• If Insite == False (True by default) the method returns a modified copy of self.relation without altering the original self.relation, otherwise self.relation and self.valuationdomain is modified.

convertValuationToDecimal()

Convert the float valuation limits to Decimals.

coveringIndex(choice, direction='out')

Renders the covering index of a given choice in a set of objects, ie the minimum number of choice members that cover each non selected object.

crispKDistance(digraph, Debug=False)

Renders the crisp Kendall distance between two bipolar valued digraphs.

Warning

Obsolete! Is replaced by the self.computeBipolarCorrelation(other, MedianCut=True) Digraph method

detectChordlessCircuits(Comments=False, Debug=False)

Detects a chordless circuit in a digraph. Returns a Boolean

detectChordlessPath(Pk, n2, Comments=False, Debug=False)

New procedure from Agrum study April 2009 recursive chordless path extraction starting from path Pk = [n2, …., n1] and ending in node n2. Optimized with marking of visited chordless P1s.

detectCppChordlessCircuits(Debug=False)

python wrapper for the C++/Agrum based chordless circuits detection exchange arguments with external temporary files.

Returns a boolean value

Warning

Deprecated !!! The python vesion is more efficient

determinateness(vec, inPercent=True)

Renders the determinateness of a characteristic vector vec = [(r(x),x),(r(y),y), …] of length n in valuationdomain [Min,Med,Max]:

result = sum_x( abs(r(x)-Med) ) / ( n*(Max-Med) )

If inPercent, result shifted (+1) and reduced (/2) to [0,1] range.

digraph2Graph(valuationDomain={'max': 1, 'med': 0, 'min': -1}, Debug=False, ConjunctiveConversion=True)

Convert a Digraph instance to a Graph instance.

dneighbors(node)

Renders the set of dominated out-neighbors of a node.

domin(choice)

Renders the dominance degree of a choice.

dominantChoices(S)

Generates all minimal dominant choices of a bipolar valued digraph.

Note

Initiate with S = self.actions.copy().

domirred(choice)

Renders the crips +irredundance degree of a choice.

domirredval(choice, relation)

Renders the valued +irredundance degree of a choice.

domirredx(choice, x)

Renders the crips +irredundance degree of node x in a choice.

domkernelrestrict(prekernel)

Parameter: dominant prekernel Renders dominant prekernel restricted relation.

exportGraphViz(fileName=None, actionsSubset=None, bestChoice={}, worstChoice={}, firstChoice={}, lastChoice={}, Comments=True, graphType='png', pictureFormat=None, graphSize='7,7', relation=None, bgcolor='cornsilk')

export GraphViz dot file for graph drawing filtering.

exportPrincipalImage(plotFileName=None, pictureFormat='pdf', bgcolor='cornsilk', fontcolor='red3', fontsize='0.75', Reduced=False, Colwise=False, tempDir='.', Comments=False)

Export as PDF (default) the principal projection of the valued relation using the three principal eigen vectors.

Implemeted picture formats are: ‘pdf’ (default), ‘png’, ‘jpeg’ and ‘xfig’.

The background color is set by default to ‘cornsilk’.

Font size and color are set by default to ‘red3’, resp. ‘0.75’.

When Reduced==True, the valued relation characeteristics are centered and reduced.

When Colwise==True, the column vectors of the adjacency table are used for the principal projection, otherwise the rows (default) are used. Has no incidence when the Digraph instance self is symmetric.

Warning

The method, writing and reading temporary files: tempCol.r and rotationCol.csv, resp. tempRow.r and rotationRow.csv, by default in the working directory (./), is hence not safe for multiprocessing programs, unless a temporary directory tempDir is provided.

flatChoice(ch, Debug=False)

Converts set or list ch recursively to a flat list of items.

forcedBestSingleChoice()

Renders the set of most determined outranking singletons in self.

gammaSets()

Renders the dictionary of neighborhoods {node: (dx,ax)} with set dx gathering the dominated, and set ax gathering the absorbed neighborhood.

generateAbsPreKernels()

Generate all absorbent prekernels from independent choices generator.

generateDomPreKernels()

Generate all dominant prekernels from independent choices generator.

htmlChoiceVector(ch, ChoiceVector=True, choiceType='good')

Show procedure for annotated bipolar choices.

inDegrees()

renders the median cut indegrees

inDegreesDistribution()

Renders the distribution of indegrees.

independentChoices(U)

Generator for all independent choices with neighborhoods of a bipolar valued digraph:

Note

• Initiate with U = self.singletons().

• Yields [(independent choice, domnb, absnb, indnb)].

inner_prod(v1, v2)

Parameters: two choice characteristic vectors Renders the inner product of two characteristic vetors.

intstab(choice)

Computes the independence degree of a choice.

irreflex(mat)

Puts diagonal entries of mat to valuationdomain[‘min’]

isAsymmetricIndeterminate(Debug=False)

Checks the self.relation for assymmetric indeterminateness!!

Warning

The reflexive links are ignored !!

isComplete(Debug=False)

checks the completeness property of self.relation by checking for the absence of a link between two actions!!

Warning

The reflexive links are ignored !!

isCyclic(Debug=False)

checks the cyclicity of self.relation by checking for a reflexive loop in its transitive closure-

Warning

self.relation is supposed to be irreflexive !

isIntegerValued(Debug=False)

Checks whether the decimal valuation of self is integer-valued be using the as_integer_ratio() method of a Decimal giving a tuple (numerator,denominator). If denominator == 1, the number is an integer.

isOutrankingDigraph(Comments=True, Debug=False)

Checks the outranking digraph characteristic condition (3.3).

relation[x][y] + relation[y][x)[y] >= 0.0

Warning

The reflexive links are ignored and the valuation must be bipolar !!

isStrictOutrankingDigraph(Comments=True, Debug=False)

Checks the strict outranking digraph characteristic condition (3.1).

-(relation[x][y] + relation[y][x]) <= 0.0 , x != y

Warning

The reflexive links are ignored and the valuation must be bipolar !!

isSymmetric(Comments=False)

True if symmetry degree == 1.0.

isTransitive(Comments=False)

True if transitivity degree == 1.0.

isWeaklyComplete(Debug=False)

checks the weakly completeness property of self.relation by checking for the absence of a link between two actions!!

Warning

The reflexive links are ignored !!

iterateRankingByChoosing(Odd=False, CoDual=False, Comments=True, Debug=False, Limited=None)

Renders a ranking by choosing result when progressively eliminating all chordless (odd only) circuits with rising valuation cut levels.

Parameters

CoDual = False (default)/True Limited = proportion (in [0,1]) * (max - med) valuationdomain

kChoices(A, k)

Renders all choices of length k from set A

matmult2(m, v)

Parameters: digraph relation and choice characteristic vector matrix multiply vector by inner production

meanDegree()

Renders the mean degree of self. !!! self.size must be set previously !!!

meanLength(Oriented=False)

Renders the (by default non-oriented) mean neighbourhoor depth of self. !!! self.order must be set previously !!!

minimalChoices(S)

Generates all dominant or absorbent choices of a bipolar valued digraph.

minimalValuationLevelForCircuitsElimination(Odd=True, Debug=False, Comments=False)

renders the minimal valuation level <lambda> that eliminates all self.circuitsList stored odd chordless circuits from self.

Warning

The <lambda> level polarised may still contain newly appearing chordless odd circuits !

neighbourhoodCollection(Oriented=False, Potential=False)

Renders the neighbourhood.

neighbourhoodDepthDistribution(Oriented=False)

Renders the distribtion of neighbourhood depths.

notGammaSets()

Renders the dictionary of neighborhoods {node: (dx,ax)} with set dx gathering the not dominated, and set ax gathering the not absorbed neighborhood.

notaneighbors(node)

Renders the set of absorbed not in-neighbors of a node.

notdneighbors(node)

Renders the set of not dominated out-neighbors of a node.

outDegrees()

renders the median cut outdegrees

outDegreesDistribution()

Renders the distribution of outdegrees.

plusirredundant(U)

Generates all +irredundant choices of a digraph.

powerset(U)

Generates all subsets of a set.

readPerrinMisset(file='curd.dat')

read method for 0-1-char-coded MISs by default from the perrinMIS.c curd.dat result file.

readabsvector(x, relation)

Parameter: action x absorbent in vector.

readdomvector(x, relation)

Parameter: action x dominant out vector.

recodeValuation(newMin=-1.0, newMax=1.0, ndigits=4, Debug=False)

Recodes the characteristic valuation domain according to the parameters given.

ndigits indicates the number of decimal digits of the valuation.

relationFct(x, y)

wrapper for self.relation dictionary access to ensure interoperability with the sparse and big outranking digraph implementation model.

save(fileName='tempdigraph', option=None, DecimalValuation=True, decDigits=2)

Persistent storage of a Digraph class instance in the form of a python source code file

saveCSV(fileName='tempdigraph', Normalized=False, Dual=False, Converse=False, Diagonal=False, Debug=False)

Persistent storage of a Digraph class instance in the form of a csv file.

saveXMCDA2(fileName='temp', fileExt='xmcda2', Comments=True, relationName='R', relationType='binary', category='random', subcategory='valued', author='digraphs Module (RB)', reference='saved from Python', valuationType='standard', digits=2, servingD3=False)

save digraph in XMCDA 2.0 format. Deprecated now.

savedre(fileName='temp')

save digraph in nauty format.

sharp(x, y)

Paramaters: choice characteristic values. Renders the sharpest of two characteristic values x and y.

sharpvec(v, w)

Paramaters: choice characteristic vectors. Renders the sharpest of two characteristic vectors v and w.

showActions()

presentation methods for digraphs actions

showAll()

Detailed show method for genuine digraphs.

showAttributes()

Prints out the attributes of self.

showAutomorphismGenerators()

Renders the generators of the automorphism group.

showBadChoices(Recompute=True)

Characteristic values for potentially bad choices.

showBestChoiceRecommendation(Verbose=False, Comments=True, ChoiceVector=False, CoDual=True, Debug=False, _OldCoca=False, BrokenCocs=True, Cpp=False)

Shows the RuBis best choice recommendation.

Note

Computes by default the Rubis best choice recommendation on the corresponding strict (codual) outranking digraph.

By default, with BrokenCocs=True, we brake all chordless circuits at their weakest determined ( abs(r(x>y)) + abs(r(y>x)) ) link.

When BrokenCocs=False we proceed like follows:

In case of chordless circuits, if supporting arcs are more credible than the reversed negating arcs, we collapse the circuits into hyper nodes. Inversely, if supporting arcs are not more credible than the reversed negating arcs, we brake the circuits on their weakest arc.

Usage example:

>>> from outrankingDigraphs import *
>>> t = Random3ObjectivesPerformanceTableau(seed=5)
>>> g = BipolarOutrankingDigraph(t)
>>> g.showBestChoiceRecommendation()
***********************
RuBis Best Choice Recommendation (BCR)
(in decreasing order of determinateness)   
Credibility domain:  [-100.0, 100.0]
=== >> potential first choices
* choice              : ['a04', 'a14', 'a19', 'a20']
   independence        : 1.19
   dominance           : 4.76
   absorbency          : -59.52
   covering (%)        : 75.00
   determinateness (%) : 57.86
   - most credible action(s) = { 'a14': 23.81, 'a19': 11.90, 'a04': 2.38, 'a20': 1.19, }  
=== >> potential last choices 
* choice              : ['a03', 'a12', 'a17']
  independence        : 4.76
  dominance           : -76.19
  absorbency          : 4.76
  covering (%)        : 0.00
  determinateness (%) : 65.39
  - most credible action(s) = { 'a03': 38.10, 'a12': 13.10, 'a17': 4.76, }
Execution time: 0.024 seconds
*****************************

showChoiceVector(ch, choiceType='good', ChoiceVector=True)

Show procedure for annotated bipolar choices.

showChordlessCircuits(Recompute=False)

Show method for chordless circuits observed in a Digraph instance.

If previous computation is required, stores the detected circuits in self.circuitsList attribute.

showComponents()

Shows the list of connected components of the digraph instance.

showCorrelation(corr=None, ndigits=3)

Renders the valued ordinal correlation index, the crisp Kendall tau index and their epistemic determination degree.

showFirstChoiceRecommendation(Verbose=False, Comments=True, ChoiceVector=False, CoDual=True, Debug=False, _OldCoca=False, BrokenCocs=True, Cpp=False)

Shows the RuBis first choice recommendation.

Note

Computes by default the Rubis first choice recommendation on the corresponding strict (codual) outranking digraph.

By default, with BrokenCocs=True, we brake all chordless circuits at their weakest determined ( abs(r(x>y)) + abs(r(y>x)) ) link.

When BrokenCocs=False we proceed like follows:

In case of chordless circuits, if supporting arcs are more credible than the reversed negating arcs, we collapse the circuits into hyper nodes. Inversely, if supporting arcs are not more credible than the reversed negating arcs, we brake the circuits on their weakest arc.

Usage example:

>>> from outrankingDigraphs import *
>>> t = Random3ObjectivesPerformanceTableau(seed=5)
>>> g = BipolarOutrankingDigraph(t)
>>> g.showFirstChoiceRecommendation()
***********************
RuBis First Choice Recommendation (BCR)
(in decreasing order of determinateness)   
Credibility domain:  [-100.0, 100.0]
=== >> potential first choices
* choice              : ['a04', 'a14', 'a19', 'a20']
   independence        : 1.19
   dominance           : 4.76
   absorbency          : -59.52
   covering (%)        : 75.00
   determinateness (%) : 57.86
   - most credible action(s) = { 'a14': 23.81, 'a19': 11.90, 'a04': 2.38, 'a20': 1.19, }  
=== >> potential last choices 
* choice              : ['a03', 'a12', 'a17']
  independence        : 4.76
  dominance           : -76.19
  absorbency          : 4.76
  covering (%)        : 0.00
  determinateness (%) : 65.39
  - most credible action(s) = { 'a03': 38.10, 'a12': 13.10, 'a17': 4.76, }
Execution time: 0.024 seconds
*****************************

showGoodChoices(Recompute=True)

Characteristic values for potentially good choices.

showHTMLRelationHeatmap(actionsList=None, rankingRule='NetFlows', colorLevels=7, tableTitle='Relation Heatmap', relationName='r(x S y)', ndigits=2, fromIndex=None, toIndex=None, htmlFileName=None)

Launches a browser window with the colored relation map of self.

See corresponding showHTMLRelationMap method.

The colorLevels parameter may be set to 3, 5, 7 (default) or 9.

When the actionsList parameter is None (default), the digraphs actions list may be ranked with the rankingRule parameter set to the ‘Copeland’ (default) or to the ‘Netlows’ ranking rule.

When the htmlFileName parameter is set to a string value ‘xxx’, a html file named ‘xxx.html’ will be generated in the current working directory. Otherwise, a temporary file named ‘tmp*.html’ will be generated there.

Example:

>>> from outrankingDigraphs import *
>>> t = RandomCBPerformanceTableau(numberOfActions=25,seed=1)
>>> g = BipolarOutrankingDigraph(t,ndigits=2)
>>> gcd = ~(-g)  # strict outranking relation
>>> gcd.showHTMLRelationHeatmap(colorLevels=7,ndigits=2)

showHTMLRelationMap(actionsList=None, rankingRule='Copeland', Colored=True, tableTitle='Relation Map', relationName='r(x S y)', symbols=['+', '&middot;', '&nbsp;', '&#150;', '&#151'], fromIndex=None, toIndex=None, htmlFileName=None)

Launches a browser window with the colored relation map of self. See corresponding Digraph.showRelationMap() method.

When htmlFileName parameter is set to a string value, a html file with that name will be stored in the current working directory.

By default, a temporary file named: tmp*.html will be generated instead in the current working directory.

Example:

>>> from outrankingDigraphs import *
>>> t = RandomCBPerformanceTableau(numberOfActions=25,seed=1)
>>> g = BipolarOutrankingDigraph(t,Normalized=True)
>>> gcd = ~(-g)  # strict outranking relation
>>> gcd.showHTMLRelationMap(rankingRule="NetFlows")

showHTMLRelationTable(actionsList=None, relation=None, IntegerValues=False, ndigits=2, Colored=True, tableTitle='Valued Adjacency Matrix', relationName='r(x S y)', ReflexiveTerms=False, htmlFileName=None, fromIndex=None, toIndex=None)

Launches a browser window with the colored relation table of self.

showMIS(withListing=True)

Prints all maximal independent choices:

Result in self.misset.

showMIS_AH(withListing=True)

Prints all MIS using the Hertz method.

Result saved in self.hertzmisset.

showMIS_HB2(withListing=True)

Prints all MIS using the Hertz-Bisdorff method.

Result saved in self.newmisset.

showMIS_RB(withListing=True)

Prints all MIS using the Bisdorff method.

Result saved in self.newmisset.

showMIS_UD(withListing=True)

Prints all MIS using the Hertz-Bisdorff method.

Result saved in self.newmisset.

showMaxAbsIrred(withListing=True)

Computing maximal -irredundant choices:

Result in self.absirset.

showMaxDomIrred(withListing=True)

Computing maximal +irredundant choices:

Result in self.domirset.

showMinAbs(withListing=True)

Prints minimal absorbent choices:

Result in self.absset.

showMinDom(withListing=True)

Prints all minimal dominant choices:

Result in self.domset.

showNeighborhoods()

Lists the gamma and the notGamma function of self.

showOrbits(InChoices, withListing=True)

Prints the orbits of Choices along the automorphisms of the Digraph instance.

Example Python session for computing the non isomorphic MISs from the 12-cycle graph:

>>> from digraphs import *
>>> c12 = CirculantDigraph(order=12,circulants=[1,-1])
>>> c12.automorphismGenerators()
...
  Permutations
  {'1': '1', '2': '12', '3': '11', '4': '10', '5': 
   '9', '6': '8', '7': '7', '8': '6', '9': '5', '10': 
   '4', '11': '3', '12': '2'}
  {'1': '2', '2': '1', '3': '12', '4': '11', '5': '10', 
   '6': '9', '7': '8', '8': '7', '9': '6', '10': '5', 
   '11': '4', '12': '3'}
  Reflections {}
>>> print('grpsize = ', c12.automorphismGroupSize)
  grpsize = 24
>>> c12.showMIS(withListing=False)
  *---  Maximal independent choices ---*
  number of solutions:  29
  cardinality distribution
  card.:  [0, 1, 2, 3, 4,  5,  6, 7, 8, 9, 10, 11, 12]
  freq.:  [0, 0, 0, 0, 3, 24,  2, 0, 0, 0,  0,  0,  0]
  Results in c12.misset
>>> c12.showOrbits(c12.misset,withListing=False)
...
  *---- Global result ----
  Number of MIS:  29
  Number of orbits :  4
  Labelled representatives:
  1: ['2','4','6','8','10','12']
  2: ['2','5','8','11']
  3: ['2','4','6','9','11']
  4: ['1','4','7','9','11']
  Symmetry vector
  stabilizer size: [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...]
  frequency      : [0, 2, 0, 0, 0, 0, 0, 1, 0,  0,  0,  1, ...]

Figure: The symmetry axes of the non isomorphic MISs of the 12-cycle:

Reference: R. Bisdorff and J.L. Marichal (2008). Counting non-isomorphic maximal independent sets of the n-cycle graph. Journal of Integer Sequences, Vol. 11 Article 08.5.7 (openly accessible here)

showOrbitsFromFile(InFile, withListing=True)

Prints the orbits of Choices along the automorphisms of the digraph self by reading in the 0-1 misset file format. See the digraphs.Digraph.readPerrinMisset() method.

showPreKernels(withListing=True)

Printing dominant and absorbent preKernels:

Result in self.dompreKernels and self.abspreKernels

showRankingByBestChoosing(rankingByBestChoosing=None)

A show method for self.rankinByBestChoosing result.

Warning

The self.computeRankingByBestChoosing(CoDual=False/True) method instantiating the self.rankingByBestChoosing slot is pre-required !

showRankingByChoosing(rankingByChoosing=None, WithCoverCredibility=False)

A show method for self.rankinByChoosing result.

When parameter WithCoverCredibility is set to True, the credibility of outranking, respectively being outranked is indicated at each selection step.

Warning

The self.computeRankingByChoosing(CoDual=False/True) method instantiating the self.rankingByChoosing slot is pre-required !

showRankingByLastChoosing(rankingByLastChoosing=None, Debug=None)

A show method for self.rankinByChoosing result.

Warning

The self.computeRankingByLastChoosing(CoDual=False/True) method instantiating the self.rankingByChoosing slot is pre-required !

showRelation()

prints the relation valuation in ##.## format.

showRelationMap(symbols=None, rankingRule='Copeland', fromIndex=None, toIndex=None, actionsList=None)

Prints on the console, in text map format, the location of certainly validated and certainly invalidated outranking situations.

By default, symbols = {‘max’:’┬’,’positive’: ‘+’, ‘median’: ‘ ‘,

‘negative’: ‘-’, ‘min’: ‘┴’}

The default ordering of the output is following the Copeland ranking rule from best to worst actions. Further available ranking rule is the ‘NetFlows’ net flows rule.

Example:

>>> from outrankingDigraphs import *
>>> t = RandomCBPerformanceTableau(numberOfActions=25,seed=1)
>>> g = BipolarOutrankingDigraph(t,Normalized=True)
>>> gcd = ~(-g)  # strict outranking relation
>>> gcd.showRelationMap(rankingRule="NetFlows")
 -   ++++++++  +++++┬+┬┬+
- -   + +++++ ++┬+┬+++┬++
┴+  ┴ + ++  ++++┬+┬┬++┬++
-   ++ - ++++-++++++┬++┬+
   - - - ++- ┬- + -+┬+-┬┬
-----  -      -┬┬┬-+  -┬┬
----    --+-+++++++++++++
-- --+- --++ ++ +++-┬+-┬┬
----  -  -+-- ++--+++++ +
----- ++- --- +---++++┬ +
-- -- ---+ -++-+++-+ +-++
-- --┴---+  + +-++-+ -  +
---- ┴---+-- ++--++++ - +
  --┴┴--  --- -  --+ --┬┬
 ---------+--+ ----- +-┬┬
-┴---┴- ---+- + ---+++┬ +
-┴┴--┴---+--- ++ -++--+++
-----┴--- ---+-+- ++---+ 
-┴┴--------------- --++┬ 
--┴---------------- --+┬ 
┴--┴┴ -┴--┴┴-┴ --++  ++-+
----┴┴--------------- -  
┴┴┴----+-┴+┴---┴-+---+ ┴+
┴┴-┴┴┴-┴- - -┴┴---┴┴+ ┬ -
----┴┴-┴-----┴┴---  - -- 
Ranking rule: NetFlows
>>> 

showRelationTable(Sorted=True, rankingRule=None, IntegerValues=False, actionsSubset=None, relation=None, ndigits=2, ReflexiveTerms=True, fromIndex=None, toIndex=None)

Prints the relation valuation in actions X actions table format. Copeland and NetFlows rankings my be used.

showRubisBestChoiceRecommendation(**kwargs)

Dummy for backward portable showBestChoiceRecommendation().

showRubyChoice(Verbose=False, Comments=True, _OldCoca=True)

Dummy for showBestChoiceRecommendation() needed for older versions compatibility.

showShort()

concise presentation method for genuine digraphs.

showSingletonRanking(Comments=True, Debug=False)

Calls self.computeSingletonRanking(comments=True,Debug = False). Renders and prints the sorted bipolar net determinatation of outrankingness minus outrankedness credibilities of all singleton choices.

res = ((netdet,sigleton,dom,absorb)+)

showStatistics()

Computes digraph statistics like order, size and arc-density.

showdre()

Shows relation in nauty format.

singletons()

list of singletons and neighborhoods [(singx1, +nx1, -nx1, not(+nx1 or -nx1)),…. ]

sizeSubGraph(choice)

Output: (size, undeterm,arcDensity). Renders the arc density of the induced subgraph.

strongComponents(setPotential=False)

Renders the set of strong components of self.

symDegreesDistribution()

Renders the distribution of symmetric degrees.

topologicalSort(Debug=False)

If self is acyclic, adds topological sort number to each node of self and renders ordered list of nodes. Otherwise renders None. Source: M. Golumbic Algorithmic Graph heory and Perfect Graphs, Annals Of Discrete Mathematics 57 2nd Ed. , Elsevier 2004, Algorithm 2.4 p.44.

weakAneighbors(node)

Renders the set of absorbed in-neighbors of a node.

weakCondorcetLosers()

Renders the set of decision actions x such that self.relation[x][y] <= self.valuationdomain[‘med’] for all y != x.

weakCondorcetWinners()

Renders the set of decision actions x such that self.relation[x][y] >= self.valuationdomain[‘med’] for all y != x.

weakDneighbors(node)

Renders the set of dominated out-neighbors of a node.

weakGammaSets()

Renders the dictionary of neighborhoods {node: (dx,ax)}

zoomValuation(zoomFactor=1.0)

Zooms in or out, depending on the value of the zoomFactor provided, the bipolar valuation of a digraph.

class digraphs.DualDigraph(other)

Instantiates the dual ( = negated valuation) Digraph object from a deep copy of a given other Digraph instance.

The relation constructor returns the dual (negation) of self.relation with generic formula:

relationOut[a][b] = Max - self.relation[a][b] + Min, where Max (resp. Min) equals valuation maximum (resp. minimum).

Note

In a bipolar valuation, the dual operator corresponds to a simple changing of signs.

class digraphs.EmptyDigraph(order=5, valuationdomain=(-1.0, 1.0))

Parameters:

order > 0 (default=5); valuationdomain =(Min,Max).

Specialization of the general Digraph class for generating temporary empty graphs of given order in {-1,0,1}.

class digraphs.EquivalenceDigraph(d1, d2, Debug=False)

Instantiates the logical equivalence digraph of two bipolar digraphs d1 and d2 of same order. Returns None if d1 and d2 are of different order

computeCorrelation()

Renders a dictionary with slots: ‘correlation’ (tau) and ‘determination’ (d), representing the ordinal correlation between the two digraphs d1 and d2 given as arguments to the EquivalenceDigraph constructor.

See the corresponding advanced topic in the Digraph3 documentation.

class digraphs.FusionDigraph(dg1, dg2, operator='o-max', weights=None)

Instantiates the epistemic fusion of two given Digraph instances called dg1 and dg2.

Parameter:

• operator := “o-max (default)” | “o-min | o-average” : symmetrix disjunctive, resp. conjunctive, resp. avarage fusion operator.

• weights := [a,b]: if None weights = [1,1]

class digraphs.FusionLDigraph(L, operator='o-max', weights=None)

Instantiates the epistemic fusion a list L of Digraph instances.

Parameter:

• operator := “o-max” (default) | “o-min” | “o-average: epistemic disjunctive, conjunctive or symmetric average fusion.

• weights := [a,b, …]: len(weights) matching len(L). If None, weights = [1 for i in range(len(L))].

class digraphs.GraphBorder(other, Debug=False)

Instantiates the partial digraph induced by its border, i.e. be the union of its initial and terminal kernels.

class digraphs.GraphInner(other, Debug=False)

Instantiates the partial digraph induced by the complement of its border, i.e. the nodes not included in the union of its initial and terminal kernels.

class digraphs.GridDigraph(n=5, m=5, valuationdomain={'max': 1.0, 'min': -1.0}, hasRandomOrientation=False, hasMedianSplitOrientation=False)

Specialization of the general Digraph class for generating temporary Grid digraphs of dimension n times m.

Parameters:

n,m > 0; valuationdomain ={‘min’:m, ‘max’:M}.

Default instantiation (5 times 5 Grid Digraph):

n = 5, m=5, valuationdomain = {‘min’:-1.0,’max’:1.0}.

Randomly orientable with hasRandomOrientation=True (default=False).

showShort()

concise presentation method for genuine digraphs.

class digraphs.IndeterminateDigraph(other=None, nodes=None, order=5, valuationdomain=(-1, 1))

Parameters: order > 0; valuationdomain =(Min,Max). Specialization of the general Digraph class for generating temporary empty graphs of order 5 in {-1,0,1}.

class digraphs.KneserDigraph(n=5, j=2, valuationdomain={'max': 1.0, 'min': -1.0})

Specialization of the general Digraph class for generating temporary Kneser digraphs

Parameters:

n > 0; n > j > 0;

valuationdomain ={‘min’:m, ‘max’:M}.

Default instantiation as Petersen graph:

n = 5, j = 2, valuationdomain = {‘min’:-1.0,’max’:1.0}.

showShort()

concise presentation method for genuine digraphs.

class digraphs.PolarisedDigraph(digraph=None, level=None, KeepValues=True, AlphaCut=False, StrictCut=False)

Renders the polarised valuation of a Digraph class instance:

Parameters:

• If level = None, a default strict 50% cut level (0 in a normalized [-1,+1] valuation domain) is used.

• If KeepValues = False, the polarisation results in a crisp {-1,0,1}-valued result.

• If AlphaCut = True a genuine one-sided True-oriented cut is operated.

• If StrictCut = True, the cut level value is excluded resulting in an open polarised valuation domain. By default the polarised valuation domain is closed and the complementary indeterminate domain is open.

class digraphs.RedhefferDigraph(order=5, valuationdomain=(-1.0, 1.0))

Specialization of the general Digraph class for generating temporary Redheffer digraphs.

https://en.wikipedia.org/wiki/Redheffer_matrix

Parameters:

order > 0; valuationdomain=(Min,Max).

class digraphs.StrongComponentsCollapsedDigraph(digraph=None)

Reduction of Digraph object to its strong components.

showComponents()

Shows the list of connected components of the digraph instance.

class digraphs.SymmetricPartialDigraph(digraph)

Renders the symmetric part of a Digraph instance.

Note

• The not symmetric and the reflexive links are all put to the median indeterminate characteristics value!.

• The constructor makes a deep copy of the given Digraph instance!

class digraphs.XMCDA2Digraph(fileName='temp')

Specialization of the general Digraph class for reading stored XMCDA-2.0 formatted digraphs. Using the inbuilt module xml.etree (for Python 2.5+).

Param:

fileName (without the extension .xmcda).

showAll()

Detailed show method for genuine digraphs.

class digraphs.XORDigraph(d1, d2, Debug=False)

Instantiates the XOR digraph of two bipolar digraphs d1 and d2 of same order.

class digraphs.kChoicesDigraph(digraph=None, k=3)

Specialization of general Digraph class for instantiation a digraph of all k-choices collapsed actions.

Parameters:

digraph := Stored or memory resident digraph instance

k := cardinality of the choices

Back to the Table of Contents

---

2.4. randomDigraphs module

Inheritance Diagram

Python3+ implementation of some models of random digraphs Based on Digraphs3 ressources Copyright (C) 2015-2023 Raymond Bisdorff

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

class randomDigraphs.RandomDigraph(order=9, arcProbability=0.5, IntegerValuation=True, Bipolar=True, seed=None)

Specialization of the general Digraph class for generating temporary crisp (irreflexive) random crisp digraphs.

Parameters:

• order (default = 10);

• arcProbability (in [0.,1.], default=0.5)

• IntegerValuation (default = True);

• If Bipolar=True, valuation domain = {-1,1} otherwise = {0,1}

• If seed is not None, the random generator is seeded

class randomDigraphs.RandomFixedDegreeSequenceDigraph(order=7, degreeSequence=[3, 3, 2, 2, 1, 1, 0], seed=None)

Specialization of the general Digraph class for generating temporary random crisp graphs (symmetric digraphs) with a fixed sequence of degrees.

Parameters:

order=n and degreeSequence=[degree_1, … ,degree_n]>

Warning

The implementation is not guaranteeing a uniform choice among all potential valid graph instances.

class randomDigraphs.RandomFixedSizeDigraph(order=7, size=14, seed=None)

Generates a random crisp digraph with a fixed size, by instantiating a fixed numbers of arcs from random choices in the set of potential oriented pairs of nodes numbered from 1 to order.

class randomDigraphs.RandomGridDigraph(n=5, m=5, valuationdomain={'max': 1.0, 'min': -1.0}, seed=None, Debug=False)

Specialization of the general Digraph class for generating temporary randomly oriented Grid digraphs of dimension n time m (default 5x5).

Parameters:

• n,m > 0;

• valuationdomain ={‘min’:-1 (default),’max’: 1 (default)}.

class randomDigraphs.RandomOutrankingValuationDigraph(order=5, weightsSum=10, distribution='uniform', incomparabilityProbability=0.1, polarizationProbability=0.05, ndigits=4, seed=None, Debug=False)

Specialization of the general Digraph class for generating temporary uniform random outranking valuation digraphs.

Note

The valuation verifies the characteristic condition: r(x,y) >= -r(y,x) for x neq y

Parameters:

• weightsSum := integer (default = 10), supposed sum of criteria significance weights)

• distribution := ‘uniform’ (default) | ‘triangular’

• incomparabilityProbability := float (default = 0.05),

• polarizationProbability := float (default = 0.05).

class randomDigraphs.RandomPartialTournament(order=10, ndigits=2, Crisp=True, missingRelationProbability=0.3, seed=None, Debug=False)

Specialization of the general Digraph class for generating temporary partial tournaments.

Parameter:

• order = n > 0

• If valuationDomain = None, valuation is normalized (in [-1.0,1.0])

• If is Crips = True, valuation is polarized to min and max values

class randomDigraphs.RandomRegularDigraph(order=7, degree=2, seed=None)

Specialization of Digraph class for random regular symmetric instances.

Parameters:

order and degree.

class randomDigraphs.RandomTournament(order=10, ndigits=2, Crisp=True, valuationDomain=[-1, 1], seed=None)

Specialization of the general Digraph class for generating temporary complete tournaments.

Parameter:

• order = n > 0

• If valuationDomain = None, valuation is normalized (in [-1.0,1.0])

• If is Crips = True, valuation is polarized to min and max values

class randomDigraphs.RandomValuationDigraph(order=9, ndigits=2, Normalized=True, IntegerValuation=False, seed=None)

Specialization of the general Digraph class for generating temporary uniformly valuated random digraphs.

Parameters:

• order > 0, number of arcs;

• ndigits > 0, number of digits if IntegerValuation = True, otherwise number of decimals;

• Normalized = True (r in [-1,1] (default), r in [0,1] if False);

• IntegerValuation = False (default)

• If seed is not None, the random generator is seeded

Example python3 session:

>>> from randomDigraphs import RandomValuationDigraph
>>> dg = RandomValuationDigraph(order=5,Normalized=True)
>>> dg.showAll()
*----- show detail -------------*
Digraph          : randomValuationDigraph
*---- Actions ----*
['1', '2', '3', '4', '5']
*---- Characteristic valuation domain ----*
{'max': Decimal('1.0'), 'min': Decimal('-1.0'),
 'med': Decimal('0.0'), 'hasIntegerValuation': False}
* ---- Relation Table -----
  S   |  '1'    '2'    '3'    '4'     '5'     
 -----|-----------------------------------
  '1' |  0.00   0.28   0.46  -0.66   0.90    
  '2' | -0.08   0.00  -0.46  -0.42   0.52    
  '3' |  0.84  -0.10   0.00  -0.54   0.58    
  '4' |  0.90   0.88   0.90   0.00  -0.38    
  '5' | -0.50   0.64   0.42  -0.94   0.00    
*--- Connected Components ---*
1: ['1', '2', '3', '4', '5']
Neighborhoods:
  Gamma     :
'4': in => set(), out => {'1', '2', '3'}
'5': in => {'1', '2', '3'}, out => {'2', '3'}
'1': in => {'4', '3'}, out => {'5', '2', '3'}
'2': in => {'4', '5', '1'}, out => {'5'}
'3': in => {'4', '5', '1'}, out => {'5', '1'}
  Not Gamma :
'4': in => {'5', '1', '2', '3'}, out => {'5'}
'5': in => {'4'}, out => {'4', '1'}
'1': in => {'5', '2'}, out => {'4'}
'2': in => {'3'}, out => {'4', '1', '3'}
'3': in => {'2'}, out => {'4', '2'}

>>> dg.exportGraphViz()

class randomDigraphs.RandomWeakTournament(order=10, ndigits=2, IntegerValuation=False, weaknessDegree=0.25, indeterminatenessProbability=0.0, seed=None, Comments=False)

Specialization of the general Digraph class for generating temporary bipolar-valued weak, i.e. partially determinate, tournaments.

Parameters:

• order = n > 0

• weaknessDegree in [0.0,1.0]: proportion of indeterminate links (default = 0.25)

• If IntegerValuation = True, valuation domain = [-pow(10,ndigits); + pow(10,ndigits)] else valuation domain = [-1.0,1.0]

• If seed is not None, the random number generator is seeded

Back to the Table of Contents

---

2.5. perfTabs module

Inheritance Diagram

Python3 implementation of digraphs Module for working with performance tableaux Copyright (C) 2011-2023 Raymond Bisdorff

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

class perfTabs.CSVPerformanceTableau(fileName='temp', Debug=False)

Reading stored CSV encoded actions x criteria PerformanceTableau instances, Using the inbuilt module csv.

Param:

fileName (without the extension .csv).

class perfTabs.CircularPerformanceTableau(order=5, scale=(0.0, 100.0), NoPolarisation=True)

Constructor for circular performance tableaux.

class perfTabs.ConstantPerformanceTableau(inPerfTab, actionsSubset=None, criteriaSubset=None, position=0.5)

Constructor for (partially) constant performance tableaux.

Parameter:

• actionsSubset selects the actions to be set at equal constant performances,

• criteriaSubset select the concerned subset of criteria,

• The position parameter (default = median performance) selects the constant performance in the respective scale of each performance criterion.

class perfTabs.EmptyPerformanceTableau

Template for PerformanceTableau objects.

class perfTabs.NormalizedPerformanceTableau(argPerfTab=None, lowValue=0, highValue=100, coalition=None, Debug=False)

specialsation of the PerformanceTableau class for constructing normalized, 0 - 100, valued PerformanceTableau instances from a given argPerfTab instance.

class perfTabs.PartialPerformanceTableau(inPerfTab, actionsSubset=None, criteriaSubset=None, objectivesSubset=None)

Constructor for partial performance tableaux concerning a subset of actions and/or criteria and/or objectives

class perfTabs.PerformanceTableau(filePerfTab=None, isEmpty=False)

In this Digraph3 module, the root perfTabs.PerformanceTableau class provides a generic performance table model. A given object of this class consists in:

• A set of potential decision actions : an ordered dictionary describing the potential decision actions or alternatives with ‘name’ and ‘comment’ attributes,

• An optional set of decision objectives: an ordered dictionary with name, comment, weight and list of concerned criteria per objective,

• A coherent family of criteria: a ordered dictionary of criteria functions used for measuring the performance of each potential decision action with respect to the preference dimension captured by each criterion,

• The evaluation: a dictionary of performance evaluations for each decision action or alternative on each criterion function,

• The NA numerical symbol: Decimal(‘-999’) by default representing missing evaluation data.

Structure:

actions = OrderedDict([('a1', {'name': ..., 'comment': ...}),
           ('a2', {'name': ..., 'comment': ...}),
           ...])
objectives = OrderedDict([
            ('obj1', {'name': ..., 'comment': ..., 'weight': ..., 'criteria': ['g1', ...]}),
            ('obj2', {'name': ..., 'comment', ..., 'weight': ..., 'criteria': ['g2', ...]}),
            ...])
criteria = OrderedDict([
     ('g1', {'weight':Decimal("3.00"),
             'scale': (Decimal("0.00"),Decimal("100.00")),
             'thresholds' : {'pref': (Decimal('20.0'), Decimal('0.0')),
                             'ind': (Decimal('10.0'), Decimal('0.0')),
                             'veto': (Decimal('80.0'), Decimal('0.0'))},
             'objective': 'obj1',
             }),
     ('g2', {'weight':Decimal("5.00"),
             'scale': (Decimal("0.00"),Decimal("100.00")),
             'thresholds' : {'pref': (Decimal('20.0'), Decimal('0.0')),
                                   'ind': (Decimal('10.0'), Decimal('0.0')),
                                   'veto': (Decimal('80.0'), Decimal('0.0'))},
             'objective': 'obj2',
             }),
     ...])
evaluation = {'g1': {'a1':Decimal("57.28"),'a2':Decimal("99.85"), ...},
              'g2': {'a1':Decimal("88.12"),'a2':Decimal("-999"), ...},
              ...}

With the help of the perfTabs.RandomPerformanceTableau class let us generate for illustration a random performance tableau concerning 7 decision actions or alternatives denoted a01, a02, …, a07:

>>> from randomPerfTabs import RandomPerformanceTableau
>>> rt = RandomPerformanceTableau(seed=100)
>>> rt.showActions()
    *----- show decision action --------------*
    key:  a01
      short name: a01
      name:       random decision action
      comment:    RandomPerformanceTableau() generated.
    key:  a02
      short name: a02
      name:       random decision action
      comment:    RandomPerformanceTableau() generated.
    key:  a03
      short name: a03
      name:       random decision action
      comment:    RandomPerformanceTableau() generated.
    ...
    ...
    key:  a07
    name:       random decision action
    comment:    RandomPerformanceTableau() generated.

In this example we consider furthermore a family of seven equisignificant cardinal criteria functions g01, g02, …, g07, measuring the performance of each alternative on a rational scale form 0.0 to 100.00. In order to capture the evaluation’s uncertainty and imprecision, each criterion function g1 to g7 admits three performance discrimination thresholds of 10, 20 and 80 pts for warranting respectively any indifference, preference and veto situations:

>>> rt.showCriteria(IntegerWeights=True)
*----  criteria -----*
g1 RandomPerformanceTableau() instance
  Preference direction: max
  Scale = (0.00, 100.00)
  Weight = 1 
  Threshold ind : 2.50 + 0.00x ; percentile: 6.06
  Threshold pref : 5.00 + 0.00x ; percentile: 12.12
  Threshold veto : 80.00 + 0.00x ; percentile: 100.00
g2 RandomPerformanceTableau() instance
  Preference direction: max
  Scale = (0.00, 100.00)
  Weight = 1 
  Threshold ind : 2.50 + 0.00x ; percentile: 7.69
  Threshold pref : 5.00 + 0.00x ; percentile: 14.10
  Threshold veto : 80.00 + 0.00x ; percentile: 100.00
g3 RandomPerformanceTableau() instance
  Preference direction: max
  Scale = (0.00, 100.00)
  Weight = 1 
  Threshold ind : 2.50 + 0.00x ; percentile: 6.41
  Threshold pref : 5.00 + 0.00x ; percentile: 6.41
  Threshold veto : 80.00 + 0.00x ; percentile: 100.00
    ...
    ...
g7 RandomPerformanceTableau() instance
  Preference direction: max
  Scale = (0.00, 100.00)
  Weight = 1 
  Threshold ind : 2.50 + 0.00x ; percentile: 3.85
  Threshold pref : 5.00 + 0.00x ; percentile: 11.54
  Threshold veto : 80.00 + 0.00x ; percentile: 100.00

The performance evaluations of each decision alternative on each criterion are gathered in a performance tableau:

>>> rt.showPerformanceTableau()
*----  performance tableau -----*
Criteria |  'g1'    'g2'    'g3'    'g4'    'g5'    'g6'    'g7'   
Actions  |    1       1       1       1       1       1       1    
---------|-------------------------------------------------------
 'a01'   |  15.17   62.22   39.35   31.83   38.81   56.93   64.96  
 'a02'   |  44.51   44.23   32.06   69.98   67.45   65.57   79.38  
 'a03'   |  57.87   19.10   47.67   48.80   38.93   83.87   75.11  
 'a04'   |  58.00   27.73   14.81   82.88   19.26   34.99   49.30  
 'a05'   |  24.22   41.46   79.70   41.66   94.95   49.56   43.74  
 'a06'   |  29.10   22.41   67.48   12.82   65.63   79.43   15.31  
 'a07'   |   NA     21.52   13.97   21.92   48.00   42.37   59.94  
 'a08'   |  82.29   56.90   90.72   75.74    7.97   42.39   31.39  
 'a09'   |  43.90   46.37   80.16   15.45   34.86   33.75   26.80  
 'a10'   |  38.75   16.22   69.62   6.05    71.81   38.60   59.02  
 'a11'   |  35.84   21.53   45.49    9.96   31.66   57.38   40.85  
 'a12'   |  29.12   51.16   22.03   60.55   41.14   62.34   49.12  
 'a13'   |  34.79   77.01   33.83   27.88   53.58   34.95   45.20  

computeActionCriterionPerformanceDifferences(refAction, refCriterion, comments=False, Debug=False)

computes the performances differences observed between the reference action and the others on the given criterion

computeActionCriterionQuantile(action, criterion, strategy='average', Debug=False)

renders the quantile of the performance of action on criterion

computeActionQuantile(action, Debug=False)

renders the overall performance quantile of action

computeAllQuantiles(Sorted=True, Comments=False)

renders a html string showing the table of the quantiles matrix action x criterion

computeCriterionPerformanceDifferences(c, Comments=False, Debug=False)

Renders the ordered list of all observed performance differences on the given criterion.

computeDefaultDiscriminationThresholds(criteriaList=None, quantile={'ind': 10, 'pref': 20, 'veto': 80, 'weakVeto': 60}, Debug=False, Comments=False)

updates the discrimination thresholds with the percentiles from the performance differences. Parameters: quantile = {‘ind’: 10, ‘pref’: 20, ‘weakVeto’: 60, ‘veto: 80}.

computeMinMaxEvaluations(criteria=None, actions=None)

renders minimum and maximum performances on each criterion in dictionary form: {‘g’: {‘minimum’: x, ‘maximum’: x}}

computeMissingDataProportion(InPercents=False, Comments=False)

Renders the proportion of missing data, i.e. NA == Decimal(‘-999’) entries in self.evaluation.

computeNormalizedDiffEvaluations(lowValue=0.0, highValue=100.0, withOutput=False, Debug=False)

renders and csv stores (withOutput=True) the list of normalized evaluation differences observed on the family of criteria Is only adequate if all criteria have the same evaluation scale. Therefore the performance tableau is normalized to 0.0-100.0 scales.

computePerformanceDifferences(Comments=False, Debug=False, NotPermanentDiffs=True, WithMaxMin=False)

Adds to the criteria dictionary the ordered list of all observed performance differences.

computeQuantileOrder(q0=3, q1=0, Threading=False, nbrOfCPUs=1, Comments=False)

Renders a linear ordering of the decision actions from a simulation of pre-ranked outranking digraphs.

The pre-ranking simulations range by default from quantiles=q0 to quantiles=min( 100, max(10,len(self.actions)/10]) ).

The actions are ordered along a decreasing Borda score of their ranking results.

computeQuantilePreorder(Comments=True, Debug=False)

computes the preorder of the actions obtained from decreasing majority quantiles. The quantiles are recomputed with a call to the self.computeQuantileSort() method.

computeQuantileRanking(q0=3, q1=0, Threading=False, nbrOfCPUs=1, Comments=False)

Renders a linear ranking of the decision actions from a simulation of pre-ranked outranking digraphs.

The pre-ranking simulations range by default from quantiles=q0 to qantiles=min( 100, max(10,len(self.actions)/10) ).

The actions are ordered along an increasing Borda score of their ranking results.

computeQuantileSort()

shows a sorting of the actions from decreasing majority quantiles

computeQuantiles(Debug=False)

renders a quantiles matrix action x criterion with the performance quantile of action on criterion

computeRankingConsensusQuality(ranking, Comments=False, Threading=False, nbrOfCPUs=1)

Renders the marginal criteria correlations with a given ranking with summary.

computeThresholdPercentile(criterion, threshold, Debug=False)

computes for a given criterion the quantile of the performance differences of a given constant threshold.

computeVariableThresholdPercentile(criterion, threshold, Debug=False)

computes for a given criterion the quantile of the performance differences of a given threshold.

computeWeightPreorder()

renders the weight preorder following from the given criteria weights in a list of increasing equivalence lists of criteria.

computeWeightedAveragePerformances(isNormalized=False, lowValue=0.0, highValue=100.0, isListRanked=False)

Compute normalized weighted average scores by ignoring missing data. When isNormalized == True (False by default), transforms all the scores into a common 0-100 scale. A lowValue and highValue parameter can be provided for a specific normalisation.

convert2BigData()

Renders a cPerformanceTableau instance, by converting the action keys to integers and evaluations to floats, including the discrimination thresholds, the case given.

convertEvaluation2Decimal()

Convert evaluations from obsolete float format to decimal format

convertEvaluation2Float()

Convert evaluations from decimal format to float

convertInsite2BigData()

Convert in site a standard formated Performance tableau into a bigData formated instance.

convertInsite2Standard()

Convert in site a bigData formated Performance tableau back into a standard formated PerformanceTableau instance.

convertWeight2Decimal()

Convert significance weights from obsolete float format to decimal format.

convertWeight2Integer()

Convert significance weights from Decimal format to int format.

convertWeights2Negative()

Negates the weights of criteria to be minimzed.

convertWeights2Positive()

Sets negative weights back to positive weights and negates corresponding evaluation grades.

csvAllQuantiles(fileName='quantiles')

save quantiles matrix criterionxaction in CSV format

hasOddWeightAlgebra(Debug=False)

Verify if the given criteria[self][‘weight’] are odd or not. Return a Boolen value.

mpComputePerformanceDifferences(NotPermanentDiffs=True, nbrCores=None, Debug=False)

Adds to the criteria dictionary the ordered list of all observed performance differences.

normalizeEvaluations(lowValue=0.0, highValue=100.0, Debug=False)

recode the evaluations between lowValue and highValue on all criteria

quantizeCriterionEvaluations(g, q, ndigits=2, Debug=True)

q-tile evaluation of criterion q

replaceNA(newNA=None, Comments=False)

Replaces the current self.NA symbol with the newNA symbol of type <Decimal>. If newNA is None, the defauklt value Decimal(‘-999’) is used.

restoreOriginalEvaluations(lowValue=0.0, highValue=100.0, Debug=False)

recode the evaluations to their original values on all criteria

save(fileName='tempperftab', isDecimal=True, valueDigits=2, Comments=True)

Persistant storage of Performance Tableaux.

saveCSV(fileName='tempPerfTab', Sorted=True, criteriaList=None, actionsList=None, ndigits=2, Debug=False)

1 Store the performance Tableau self Actions x Criteria in CSV format.

saveXMCDA2(fileName='temp', category='XMCDA 2.0 Extended format', user='digraphs Module (RB)', version='saved from Python session', title='Performance Tableau in XMCDA-2.0 format.', variant='Rubis', valuationType='bipolar', servingD3=False, isStringIO=False, stringNA='NA', comment='produced by saveXMCDA2()', hasVeto=True)

save performance tableau object self in XMCDA 2.0 format including decision objectives, the case given.

saveXMCDA2String(fileName='temp', category='XMCDA 2.0 format', user='digraphs Module (RB)', version='saved from Python session', title='Performance Tableau in XMCDA-2.0 format.', variant='Rubis', valuationType='bipolar', servingD3=True, comment='produced by stringIO()', stringNA='NA')

save performance tableau object self in XMCDA 2.0 format. !!! obsolete: replaced by the isStringIO in the saveXMCDA2 method !!!

setObjectiveWeights(Debug=False)

Set the objective weights to the sum of the corresponding criteria significance weights.

showActions(Alphabetic=False)

presentation methods for decision actions or alternatives

showAll()

Show fonction for performance tableau

showAllQuantiles(Sorted=True)

prints the performance quantiles tableau in the session console.

showCriteria(IntegerWeights=False, Alphabetic=False, ByObjectives=False, Debug=False)

print Criteria with thresholds and weights.

showEvaluationStatistics()

renders the variance and standard deviation of the values observed in the performance Tableau.

showHTMLCriteria(criteriaSubset=None, Sorted=True, ndigits=2, title=None, htmlFileName=None)

shows the criteria in the system browser view.

showHTMLPerformanceHeatmap(actionsList=None, WithActionNames=False, fromIndex=None, toIndex=None, Transposed=False, criteriaList=None, colorLevels=7, pageTitle=None, ndigits=2, SparseModel=False, outrankingModel='standard', minimalComponentSize=1, rankingRule='NetFlows', StoreRanking=True, quantiles=None, strategy='average', Correlations=False, htmlFileName=None, Threading=False, nbrOfCPUs=None, Debug=False)

shows the html heatmap version of the performance tableau in a browser window (see perfTabs.htmlPerformanceHeatMap() method ).

Parameters:

• actionsList and criteriaList, if provided, give the possibility to show the decision alternatives, resp. criteria, in a given ordering.

• WithActionNames = True (default False) will show the action names instead of the short names or the identifyers.

• ndigits = 0 may be used to show integer evaluation values.

• colorLevels may be 3, 5, 7, or 9.

• When no actionsList is provided, the decision actions are ordered from the best to the worst. This ranking is obtained by default with the Copeland rule applied on a standard BipolarOutrankingDigraph.

• When the SparseModel flag is put to True, a sparse PreRankedOutrankingDigraph construction is used instead.

• the outrankingModel parameter (default = ‘standard’) allows to switch to alternative BipolarOutrankingDigraph constructors, like ‘confident’ or ‘robust’ models. When called from a bipolar-valued outrankingDigraph instance, outrankingModel = ‘this’ keeps the current outranking model without recomputing by default the standard outranking model.

• The minimalComponentSize allows to control the fill rate of the pre-ranked model. When minimalComponentSize = n (the number of decision actions) both the pre-ranked model will be in fact equivalent to the standard model.

• rankingRule = ‘NetFlows’ (default) | ‘Copeland’ | ‘Kohler’ | ‘RankedPairs’ | ‘ArrowRaymond’ | ‘IteratedNetFlows’ | ‘IteraredCopeland’. See tutorial on ranking mith multiple incommensurable criteria.

• when the StoreRanking flag is set to True, the ranking result is storted in self.

• Quantiles used for the pre-ranked decomposition are put by default to n (the number of decision alternatives) for n < 50. For larger cardinalities up to 1000, quantiles = n /10. For bigger performance tableaux the quantiles parameter may be set to a much lower value not exceeding usually 10.

• The pre-ranking may be obtained with three ordering strategies for the quantiles equivalence classes: ‘average’ (default), ‘optimistic’ or ‘pessimistic’.

• With Correlations = True and criteriaList = None, the criteria will be presented from left to right in decreasing order of the correlations between the marginal criterion based ranking and the global ranking used for presenting the decision alternatives.

• For large performance Tableaux, multiprocessing techniques may be used by setting Threading = True in order to speed up the computations; especially when Correlations = True.

• By default, the number of cores available, will be detected. It may be necessary in a HPC context to indicate the exact number of singled threaded cores in fact allocated to the multiprocessing job.

>>> from randomPerfTabs import RandomPerformanceTableau
>>> rt = RandomPerformanceTableau(seed=100)
>>> rt.showHTMLPerformanceHeatmap(colorLevels=5,Correlations=True)

showHTMLPerformanceQuantiles(Sorted=True, htmlFileName=None)

shows the performance quantiles tableau in a browser window.

showHTMLPerformanceTableau(actionsSubset=None, fromIndex=None, toIndex=None, isSorted=False, Transposed=False, ndigits=2, ContentCentered=True, title=None, htmlFileName=None)

shows the html version of the performance tableau in a browser window.

showPairwiseComparison(a, b, hasSymetricThresholds=True, Debug=False, isReturningHTML=False, hasSymmetricThresholds=True)

renders the pairwise comprison parameters on all criteria in html format

showPerformanceTableau(Transposed=False, actionsSubset=None, fromIndex=None, toIndex=None, Sorted=True, ndigits=2)

Print the performance Tableau.

showQuantileSort(Debug=False)

Wrapper of computeQuantilePreorder() for the obsolete showQuantileSort() method.

showRankingConsensusQuality(ranking)

shows the marginal criteria correlations with a given ranking with summary.

showStatistics(Debug=False)

show statistics concerning the evaluation distributions on each criteria.

showWeightPreorder()

Renders a preordering of the the criteria signficance weights.

class perfTabs.XMCDA2PerformanceTableau(fileName='temp', HasSeparatedWeights=False, HasSeparatedThresholds=False, stringInput=None, Debug=False)

For reading stored XMCDA 2.0 formatted instances with exact decimal numbers. Using the inbuilt module xml.etree (for Python 2.5+).

Parameters:

• fileName is given without the extension .xml or .xmcda,

• HasSeparatedWeights in XMCDA 2.0.0 encoding (default = False),

• HasSeparatedThresholds in XMCDA 2.0.0 encoding (default = False),

• stringInput: instantiates from an XMCDA 2.0 encoded string argument.

!! Obsolete by now !!

Back to the Table of Contents

---

2.6. randomPerfTabs module

A tutorial with coding examples is available here: Generating random performance tableaux with the randPerfTabs module

Inheritance Diagram

Python implementation of digraphs Module for generating random performance tableaux Copyright (C) 2015-2023 Raymond Bisdorff

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

class randomPerfTabs.Random3ObjectivesPerformanceTableau(numberOfActions=20, shortNamePrefix='p', numberOfCriteria=13, weightDistribution='equiobjectives', weightScale=None, IntegerWeights=True, OrdinalScales=False, NegativeWeights=False, negativeWeightProbability=0.0, commonScale=None, commonThresholds=None, commonMode=None, valueDigits=2, vetoProbability=0.5, missingDataProbability=0.05, NA=-999, BigData=False, seed=None, Debug=False)

For geneating random 3 objectives: Eco, Soc and Env multile-criteria performance records. Each decision action is qualified randomly as weak (-), fair (~) or good (+) on each of the three objectives.

Generator arguments:

• numberOf Actions := 20 (default)

• shortNamePrefix := ‘a’ (default)

• number of Criteria := 13 (default)

• weightDistribution := ‘equiobjectives’ (default)

  ‘equisignificant’ (weights set all to 1)

  ‘random’ (in the range 1 to numberOfCriteria)

• weightScale := [1,numerOfCriteria] (random default)

• IntegerWeights := True (default) / False

• OrdinalScales := True / False (default), if True commonScale is set to (0,10)

• NegativeWeights := True (default) / False. If False, evaluations to be minimized are negative.

• negativeWeightProbability := [0,1] (default 0.10), ‘min’ preference direction probability

• commonScale := (Min, Max)

  when commonScale is None, (Min=0.0,Max=10.0) by default if OrdinalScales == True and (Min=0.0,Max=100.0) by default otherwise

• commonThresholds := ((Ind,Ind_slope),(Pref,Pref_slope),(Veto,Veto_slope)) with

  Ind < Pref < Veto in [0.0,100.0] such that

  (Ind/100.0*span + Ind_slope*x) < (Pref/100.0*span + Pref_slope*x) < (Pref/100.0*span + Pref_slope*x)

  By default [(0.05*span,0.0),(0.10*span,0.0),(0.60*span,0.0)] if OrdinalScales=False

  By default [(0.1*span,0.0),(0.2*span,0.0),(0.8*span,0.0)] otherwise

  with span = commonScale[1] - commonScale[0].

• commonMode := [‘triangular’,’variable’,0.50] (default), A constant mode may be provided.

  [‘uniform’,’variable’,None], a constant range may be provided.

  [‘beta’,’variable’,None] (three alpha, beta combinations:

  (5.8661,2.62203),(5.05556,5.05556) and (2.62203, 5.8661)

  chosen by default for ‘good’, ‘fair’ and ‘weak’ evaluations.

  Constant parameters may be provided.

• valueDigits := 2 (default)

• vetoProbability := x in ]0.0-1.0[ (0.5 default), probability that a cardinal criterion shows a veto preference discrimination threshold.

• Debug := True / False (default)

Warning

Minimal number required of criteria is 3!

>>> from randomPerfTabs import Random3ObjectivesPerformanceTableau
>>> t = Random3ObjectivesPerformanceTableau(numberOfActions=5,numberOfCriteria=3,seed=1)
>>> t
*------- PerformanceTableau instance description ------*
Instance class   : Random3ObjectivesPerformanceTableau
Seed             : 1
Instance name    : random3ObjectivesPerfTab
# Actions        : 5
# Objectives     : 3
# Criteria       : 3
Attributes       : ['name', 'valueDigits', 'BigData', 'OrdinalScales',
                    'missingDataProbability', 'negativeWeightProbability',
                    'randomSeed', 'sumWeights', 'valuationPrecision',
                    'commonScale', 'objectiveSupportingTypes',
                    'actions', 'objectives', 'criteriaWeightMode',
                    'criteria', 'evaluation', 'weightPreorder']
>>> t.showObjectives()
*------ show objectives -------"
Eco: Economical aspect
   ec1 criterion of objective Eco 1
  Total weight: 1.00 (1 criteria)
Soc: Societal aspect
   so2 criterion of objective Soc 1
  Total weight: 1.00 (1 criteria)
Env: Environmental aspect
   en3 criterion of objective Env 1
  Total weight: 1.00 (1 criteria)
>>> t.showActions()
*----- show decision action --------------*
key:  p1
  short name:  p1
  name:       random public policy Eco+ Soc- Env+
  profile:    {'Eco': 'good', 'Soc': 'weak', 'Env': 'good'}
key:  p2
  short name:  p2
  name:       random public policy Eco~ Soc+ Env~
  profile:    {'Eco': 'fair', 'Soc': 'good', 'Env': 'fair'}
key:  p3
  short name:  p3
  name:       random public policy Eco~ Soc~ Env-
  profile:    {'Eco': 'fair', 'Soc': 'fair', 'Env': 'weak'}
key:  p4
  short name:  p4
  name:       random public policy Eco~ Soc+ Env+
  profile:    {'Eco': 'fair', 'Soc': 'good', 'Env': 'good'}
key:  p5
  short name:  p5
  name:       random public policy Eco~ Soc+ Env~
  profile:    {'Eco': 'fair', 'Soc': 'good', 'Env': 'fair'}
>>> t.showPerformanceTableau()
*----  performance tableau -----*
criteria | weights |  'p1'   'p2'   'p3'   'p4'   'p5'   
---------|---------------------------------------------
 'ec1'   |    1    | 36.29  85.17  34.49    NA   56.58  
 'so2'   |    1    | 55.00  56.33    NA   67.36  72.22  
 'en3'   |    1    | 66.58  48.71  21.59    NA     NA  
>>>

showActions(Alphabetic=False)

presentation methods for decision actions or alternatives

class randomPerfTabs.RandomAcademicPerformanceTableau(numberOfStudents=10, numberOfCourses=5, weightDistribution='random', weightScale=(1, 5), commonScale=(0, 20), ndigits=0, WithTypes=False, commonMode=('triangular', 12, 0.25), commonThresholds=None, IntegerWeights=True, BigData=False, missingDataProbability=0.0, NA=-999, seed=None, Debug=False)

For generating a temporary academic performance tableau with random grading results performances of a number of students in different academic courses (see Lecture 4: Grading of the Algorithmic decision Theory Course http://hdl.handle.net/10993/37933 )

Parameters:

• number of students,

• number of courses,

• weightDistribution := equisignificant | random (default, see RandomPerformanceTableau)

• weightScale := (1, 1 | numberOfCourses (default when random))

• IntegerWeights := Boolean (True = default)

• commonScale := (0,20) (default)

• ndigits := 0

• WithTypes := Boolean (False = default)

• commonMode := (‘triangular’,xm=14,r=0.25)

• commonThresholds (default) := {

  ‘ind’:(0,0),

  ‘pref’:(1,0),

  } (default)

When parameter WithTypes is set to True, the students are randomly allocated to one of the four categories: weak (1/6), fair (1/3), good (1/3), and excellent (1/3), in the bracketed proportions. In a default 0-20 grading range, the random range of a weak student is 0-10, of a fair student 4-16, of a good student 8-20, and of an excellent student 12-20. The random grading generator follows a double triangular probablity law with mode equal to the middle of the random range and median repartition of probability each side of the mode.

>>> from randomPerfTabs import RandomAcademicPerformanceTableau
>>> t = RandomAcademicPerformanceTableau(numberOfStudents=7,
...              numberOfCourses=5, missingDataProbability=0.03,
...              WithTypes=True, seed=100)
>>> t
 *------- PerformanceTableau instance description ------*
 Instance class   : RandomAcademicPerformanceTableau
 Seed             : 100
 Instance name    : randstudPerf
 Actions          : 7
 Criteria         : 5
 Attributes       : ['randomSeed', 'name', 'actions',
                     'criteria', 'evaluation', 'weightPreorder']
>>> t.showPerformanceTableau()
 *----  performance tableau -----*
  Courses |  'm1' 'm2' 'm3' 'm4' 'm5' 
    ECTS  |   5    1    5    4    3   
 ---------|--------------------------
    's1f' |  12   10   14   14   13  
    's2g' |  14   12   16   12   14  
    's3g' |  13   10   NA   12   17  
    's4f' |  10   13   NA   13   12  
    's5e' |  17   12   16   17   12  
    's6g' |  17   17   12   16   14  
    's7e' |  12   13   13   16   NA  
>>> t.weightPreorder
 [['m2'], ['m5'], ['m4'], ['m1', 'm3']]

The random instance generated here with seed = 100 results in a set of only excellent (2), good (3) and fair (2) student performances. We observe 3 missing grades (NA). We may show a statistical summary per course (performance criterion) with more than 5 grades.

>>> t.showStatistics()
 *-------- Performance tableau summary statistics -------*
 Instance name      : randstudPerf
 #Actions           : 7
 #Criteria          : 5
 *Statistics per Criterion*
 Criterion name       : g1
 Criterion weight     : 5
  criterion scale      : 0.00 - 20.00
  # missing evaluations : 0
  mean evaluation       : 13.57
  standard deviation    : 2.44
  maximal evaluation    : 17.00
  quantile Q3 (x_75)    : 17.00
  median evaluation     : 13.50
  quantile Q1 (x_25)    : 12.00
  minimal evaluation    : 10.00
  mean absolute difference      : 2.69
  standard difference deviation : 3.45
 Criterion name       : g2
 Criterion weight     : 1
  criterion scale      : 0.00 - 20.00
  # missing evaluations : 0
  mean evaluation       : 12.43
  standard deviation    : 2.19
  maximal evaluation    : 17.00
  quantile Q3 (x_75)    : 14.00
  median evaluation     : 12.50
  quantile Q1 (x_25)    : 11.50
  minimal evaluation    : 10.00
  mean absolute difference      : 2.29
  standard difference deviation : 3.10
 Criterion name       : g3
 Criterion weight     : 5
  criterion scale      : 0.00 - 20.00
  # missing evaluations : 2
 Criterion name       : g4
 Criterion weight     : 4
  criterion scale      : 0.00 - 20.00
  # missing evaluations : 0
  mean evaluation       : 14.29
  standard deviation    : 1.91
  maximal evaluation    : 17.00
  quantile Q3 (x_75)    : 16.25
  median evaluation     : 15.00
  quantile Q1 (x_25)    : 12.75
  minimal evaluation    : 12.00
  mean absolute difference      : 2.12
  standard difference deviation : 2.70
 Criterion name       : g5
 Criterion weight     : 3
  criterion scale      : 0.00 - 20.00
  # missing evaluations : 1
  mean evaluation       : 13.67
  standard deviation    : 1.70
  maximal evaluation    : 17.00
  quantile Q3 (x_75)    : 15.50
  median evaluation     : 14.00
  quantile Q1 (x_25)    : 12.50
  minimal evaluation    : 12.00
  mean absolute difference      : 1.78
  standard difference deviation : 2.40

showCourseStatistics(courseID, Debug=False)

show statistics concerning the grades’ distributions in the given course.

showCourses(coursesSubset=None, ndigits=0, pageTitle='List of Courses')

Print a list of the courses.

showHTMLPerformanceTableau(studentsSubset=None, isSorted=True, Transposed=False, ndigits=0, ContentCentered=True, title=None, fromIndex=None, toIndex=None, htmlFileName=None)

shows the html version of the academic performance tableau in a browser window.

showPerformanceTableau(Transposed=False, studentsSubset=None, fromIndex=None, toIndex=None, Sorted=True, ndigits=0)

Print the performance Tableau.

showStatistics()

Obsolete

showStudents(WithComments=False)

Print a list of the students.

class randomPerfTabs.RandomCBPerformanceTableau(numberOfActions=13, numberOfCriteria=7, name='randomCBperftab', weightDistribution='equiobjectives', weightScale=None, IntegerWeights=True, NegativeWeights=False, commonPercentiles=None, samplingSize=100000, commonMode=None, valueDigits=2, missingDataProbability=0.01, NA=-999, BigData=False, seed=None, Debug=False, Comments=False)

Full automatic generation of random multiple-criteria Cost-Benefit performance tableaux.

Parameters:

• If numberOfActions is None, a uniform random number between 10 and 31 of cheap, neutral or advantageous actions (equal 1/3 probability each type) actions is instantiated.

• If numberOfCriteria is None, a uniform random number between 5 and 21 of cost or benefit criteria. Cost criteria have probability 1/3, whereas benefit criteria respectively 2/3 probability to be generated. However, at least one criterion of each kind is always instantiated.

• weightDistribution := {‘equiobjectives’ (default)|’fixed’|’random’|’equisignificant’} By default, the sum of significance of the cost criteria is set equal to the sum of the significance of the benefit criteria.

• Default weightScale for ‘random’ weightDistribution is 1 - numberOfCriteria.

• If NegativeWeights = True | False (default), the performance evaluation of the criteria with a ‘min’ preference direction will be positive, otherwise they will be negative.

• Parameter commonScale is not used. The scale of cost criteria is cardinal or ordinal (0-10) with probability 1/4, respectively 3/4, whereas the scale of benefit criteria is ordinal or cardinal with probabilities 2/3, respectively 1/3.

• All cardinal criteria are evaluated with decimals between 0.0 and 100.0 wheras all ordinal criteria are evaluated with integers between 0 and 10.

• commonThresholds parameter is not used. Preference discrimination is specified as percentiles of concerned performance differences (see below).

• CommonPercentiles = {‘ind’:0.05, ‘pref’:0.10, ‘veto’:’95} are expressed in percentiles of the observed performance differences and only concern cardinal criteria.

Note

Minimal number required of criteria is 2, and minimal number required of decision actions is 6!

>>> from randomPerfTabs import RandomCBPerformanceTableau
>>> pt = RandomCBPerformanceTableau(numberOfActions=6,numberOfCriteria=3,seed=2)
>>> pt
     *------- PerformanceTableau instance description ------*
      Instance class     : RandomCBPerformanceTableau
      Seed               : 1
      Instance name      : randomCBperftab
      Actions            : 6
      Objectives         : 2
      Criteria           : 3
      NaN proportion (%) : 0.0
      Attributes         : ['randomSeed', 'name', 'digits',
                 'BigData', 'missingDataProbability', 'NA',
                 'commonPercentiles', 'samplingSize', 'Debug',
                 'actionsTypesList', 'sumWeights',
                 'valuationPrecision', 'actions', 'objectives',
                 'criteriaWeightMode', 'criteria', 'evaluation',
                 'weightPreorder']
>>> pt.showObjetives()
    *------ decision objectives -------"
     C: Costs
      c1 random cardinal cost criterion 1
      c2 random cardinal cost criterion 1
      Total weight: 2.00 (2 criteria)
     B: Benefits
      b1 random ordinal benefit criterion 2
      Total weight: 2.00 (1 criteria)
>>> pt.showCriteria()
    *----  criteria -----*
     c1 random cardinal cost criterion
      Preference direction: min
      Scale = (0.00, 100.00)
      Weight = 0.250 
      Threshold ind : 1.98 + 0.00x ; percentile: 6.67
      Threshold pref : 8.48 + 0.00x ; percentile: 13.33
      Threshold veto : 60.79 + 0.00x ; percentile: 100.00
     b1 random ordinal benefit criterion
      Preference direction: max
      Scale = (0.00, 10.00)
      Weight = 0.500 
     c2 random cardinal cost criterion
      Preference direction: min
      Scale = (0.00, 100.00)
      Weight = 0.250 
      Threshold ind : 3.34 + 0.00x ; percentile: 6.67
      Threshold pref : 4.99 + 0.00x ; percentile: 13.33
      Threshold veto : 63.75 + 0.00x ; percentile: 100.00
>>> pt.showActions
    *----- show decision action --------------*
    key:  a1
      short name: a1c
      name:       action a1
      comment:    Cost-Benefit
    key:  a2
      short name: a2c
      name:       action a2
      comment:    Cost-Benefit
    key:  a3
      short name: a3c
      name:       action a3
      comment:    Cost-Benefit
    key:  a4
      short name: a4n
      name:       action a4
      comment:    Cost-Benefit
    key:  a5
      short name: a5c
      name:       action a5
      comment:    Cost-Benefit
    key:  a6
      short name: a6a
      name:       action a6
      comment:    Cost-Benefit
>>> pt.showPerformanceTableau()
    *----  performance tableau -----*
    Criteria |  'b1'   'c1'   'c2'   
    Actions  |    2      1      1    
    ---------|-----------------------------------------
     'a1c'   |  9.00  -37.92  -7.03  
     'a2c'   |  8.00  -35.94  -28.93  
     'a3c'   |  3.00  -16.88  -23.94  
     'a4n'   |  5.00  -46.40  -43.59  
     'a5c'   |  2.00  -26.61  -67.44  
     'a6a'   |  2.00  -77.67  -70.78  

updateDiscriminationThresholds(Comments=False, Debug=False)

Recomputes performance discrimination thresholds from commonPercentiles.

Note

Overwrites all previous criterion discrimination thresholds !

class randomPerfTabs.RandomPerformanceGenerator(argPerfTab, actionNamePrefix='a', instanceCounter=None, seed=None)

Generic wrapper for generating new decision actions or performance tableaux with random evaluations generated with a given performance tableau model of type: RandomPerformanceTableau, RandomCBPerformanceTableau, or Random3ObjectivesPerformanceTableau.

The return format of generated new set of random actions is schown below. This return may be directly feeded to the PerformanceQuantiles.updateQuantiles() method.

>>> from randomPerfTabs import *
>>> t = RandomPerformanceTableau(seed=100)
>>> t
*------- PerformanceTableau instance description ------*
Instance class   : RandomPerformanceTableau
Seed             : 100
Instance name    : randomperftab
Actions          : 13
Criteria         : 7
Attributes       : [
'randomSeed', 'name', 'BigData', 'sumWeights', 'digits', 'commonScale',
'commonMode', 'missingDataProbability', 'actions', 'criteria',
'evaluation', 'weightPreorder']
>>> rpg = RandomPerformanceGenerator(t,seed= 100)
>>> newActions = rpg.randomActions(2)
>>> print(newActions)
{'actions': OrderedDict([
('a14', {'shortName': 'a14',
         'name': 'random decision action',
         'comment': 'RandomPerformanceGenerator'}),
('a15', {'shortName': 'a15',
         'name': 'random decision action',
         'comment': 'RandomPerformanceGenerator'})]),
'evaluation': {
'g1': {'a14': Decimal('15.17'), 'a15': Decimal('80.87')},
'g2': {'a14': Decimal('44.51'), 'a15': Decimal('62.74')},
'g3': {'a14': Decimal('57.87'), 'a15': Decimal('64.24')},
'g4': {'a14': Decimal('58.0'), 'a15': Decimal('26.99')},
'g5': {'a14': Decimal('24.22'), 'a15': Decimal('21.18')},
'g6': {'a14': Decimal('29.1'), 'a15': Decimal('73.09')},
'g7': {'a14': Decimal('96.58'), 'a15': Decimal('-999')}}}
>>> newTab = rpg.randomPerformanceTableau(2)
>>> newTab.showPerformanceTableau()
*----  performance tableau -----*
criteria | weights | 'a17'   'a18'   
---------|-----------------------------------------
   'g1'  |   1   |   55.80   22.03  
   'g2'  |   1   |   57.78   33.83  
   'g3'  |   1   |   80.54   31.83  
   'g4'  |   1   |   31.15   69.98  
   'g5'  |   1   |   46.25   48.80  
   'g6'  |   1   |   42.24   82.88  
   'g7'  |   1   |   57.31   41.66  

randomActions(nbrOfRandomActions=1)

Generates nbrOfRandomActions.

randomPerformanceTableau(nbrOfRandomActions=1)

Generates nbrOfRandomActions.

class randomPerfTabs.RandomPerformanceTableau(numberOfActions=13, actionNamePrefix='a', numberOfCriteria=7, weightDistribution='equisignificant', weightScale=None, IntegerWeights=True, commonScale=(0.0, 100.0), commonThresholds=((2.5, 0.0), (5.0, 0.0), (80.0, 0.0)), commonMode=('beta', None, (2, 2)), valueDigits=2, missingDataProbability=0.025, NA=-999, BigData=False, seed=None, Debug=False)

For generating a random standard performance tableau.

Parameters:

• numberOfActions := nbr of decision actions.

• numberOfCriteria := number performance criteria.

• weightDistribution := ‘random’ (default) | ‘fixed’ | ‘equisignificant’.

  If ‘random’, weights are uniformly selected randomly

  form the given weight scale;

  If ‘fixed’, the weightScale must provided a corresponding weights

  distribution;

  If ‘equisignificant’, all criterion weights are put to unity.

• weightScale := [Min,Max] (default =[1,numberOfCriteria].

• IntegerWeights := True (default) | False (normalized to proportions of 1.0).

• commonScale := [Min;Max]; common performance measuring scales (default = [0;100])

• commonThresholds := [(q0,q1),(p0,p1),(v0,v1)]; common indifference(q), preference (p) and considerable performance difference discrimination thresholds. q0, p0 and v0 are expressed in percentige of the common scale amplitude: Max - Min.

• commonMode := common random distribution of random performance measurements (default = (‘beta’,None,(2,2)) ):

  (‘uniform’,None,None), uniformly distributed between min and max values.

  (‘normal’,mu,sigma), truncated Gaussion distribution.

  (‘triangular’,mode,repartition), generalized triangular distribution

  (‘beta’,mod,(alpha,beta)), mode in ]0,1[.

• valueDigits := <integer>, precision of performance measurements (2 decimal digits by default).

• missingDataProbability := 0 <= x <= 1.0; probability of missing performance evaluation on a criterion for an alternative (default 0.025).

• Default NA symbol == Decimal(‘-999’)

Code example:

>>> from randomPerfTabs import RandomPerformanceTableau
>>> t = RandomPerformanceTableau(numberOfActions=3,numberOfCriteria=1,seed=100)
>>> t.actions
    {'a1': {'comment': 'RandomPerformanceTableau() generated.', 'name': 'random decision action'},
     'a2': {'comment': 'RandomPerformanceTableau() generated.', 'name': 'random decision action'},
     'a3': {'comment': 'RandomPerformanceTableau() generated.', 'name': 'random decision action'}}
>>> t.criteria
    {'g1': {'thresholds': {'ind' : (Decimal('10.0'), Decimal('0.0')),
                           'veto': (Decimal('80.0'), Decimal('0.0')),
                           'pref': (Decimal('20.0'), Decimal('0.0'))},
            'scale': [0.0, 100.0],
            'weight': Decimal('1'),
            'name': 'digraphs.RandomPerformanceTableau() instance',
            'comment': 'Arguments: ; weightDistribution=random;
                weightScale=(1, 1); commonMode=None'}}
>>> t.evaluation
    {'g01': {'a01': Decimal('45.95'),
             'a02': Decimal('95.17'),
             'a03': Decimal('17.47')
            }
    }

class randomPerfTabs.RandomRankPerformanceTableau(numberOfActions=13, numberOfCriteria=7, weightDistribution='equisignificant', weightScale=None, commonThresholds=None, IntegerWeights=True, BigData=False, seed=None, Debug=False)

For generating multiple-criteria ranked (without ties) performances of a given number of decision actions. On each criterion, all decision actions are hence lineraly ordered. The randomPerfTabs.RandomRankPerformanceTableau class is matching the votingDigraphs.RandomLinearVotingProfiles class (see http://hdl.handle.net/10993/37933 Lecture 2 : Voting of the Algorithmic Decision Theory Course)

Parameters:

• number of actions,

• number of performance criteria,

• weightDistribution := equisignificant | random (default, see RandomPerformanceTableau)

• weightScale := (1, 1 | numberOfCriteria (default when random))

• IntegerWeights := Boolean (True = default). Weights are negative, as all the criteria preference directions are ‘min’, as the rank performance is to be minimized.

• commonThresholds (default) := {

  ‘ind’:(0,0),

  ‘pref’:(1,0),

  ‘veto’:(numberOfActions,0)

  } (default)

>>> t = RandomRankPerformanceTableau(numberOfActions=3,numberOfCriteria=2)
>>> t.showObjectives()
The performance tableau does not contain objectives.
>>> t.showCriteria()
*----  criteria -----*
g1 'Random criteria (voter)'
  Scale = (Decimal('0'), Decimal('3'))
  Weight = -1 # ranks to be minimal 
  Threshold ind : 0.00 + 0.00x ; percentile:  0.0
  Threshold pref : 1.00 + 0.00x ; percentile:  0.667
  Threshold veto : 3.00 + 0.00x ; percentile:  1.0
g2 'Random criteria (voter)'
  Scale = (Decimal('0'), Decimal('3'))
  Weight = -1 # ranks to be minimal
  Threshold ind : 0.00 + 0.00x ; percentile:  0.0
  Threshold pref : 1.00 + 0.00x ; percentile:  0.667
  Threshold veto : 3.00 + 0.00x ; percentile:  1.0
>>> t.showActions()
*----- show decision action --------------*
key:  a1
  short name: a1
  name:       random decision action (candidate)
  comment:    RandomRankPerformanceTableau() generated.
key:  a2
  short name: a2
  name:       random decision action (candidate)
  comment:    RandomRankPerformanceTableau() generated.
key:  a3
  short name: a3
  name:       random decision action (candidate)
  comment:    RandomRankPerformanceTableau() generated.
>>> t.showPerformanceTableau()
*----  performance tableau -----*
criteria | weights | 'a1' 'a2' 'a3'   
---------|--------------------------
   'g1'  |    -1   |   3    1    2  
   'g2'  |    -1   |   2    1    3  

Back to the Table of Contents

---

2.7. outrankingDigraphs module

A tutorial with coding examples is available here: Working with the outrankingDigraphs module

Inheritance Diagram

Python3 implementation of outranking digraphs. Copyright (C) 2006-2023 Raymond Bisdorff

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

class outrankingDigraphs.BipolarOutrankingDigraph(argPerfTab=None, objectivesSubset=None, criteriaSubset=None, coalition=None, actionsSubset=None, hasNoVeto=False, hasBipolarVeto=True, Normalized=True, ndigits=4, CopyPerfTab=True, BigData=False, Threading=False, tempDir=None, WithConcordanceRelation=True, WithVetoCounts=True, nbrCores=None, Debug=False, Comments=False)

Specialization of the abstract OutrankingDigraph root class for generating bipolarly-valued outranking digraphs.

Parameters:

• argPerfTab: instance of PerformanceTableau class. If a file name string is given, the performance tableau will directly be loaded first.

• coalition: subset of criteria to be used for contructing the outranking digraph.

• hasNoVeto: veto desactivation flag (False by default).

• hasBipolarVeto: bipolar versus electre veto activation (true by default).

• Normalized: the valuation domain is set by default to [-100,+100] (bipolar percents). If True, the valuation domain is recoded to [-1.0,+1.0].

• WithConcordanceRelation: True by default when not threading. The self.concordanceRelation contains the significance majority margin of the “at least as good relation as” without the large performance difference polarization.

• WithVetoCounts: True by default when not threading. All vetos and countervetos are stored in self.vetos and self.negativeVetos slots, as well the counts of large performance differences in self.largePerformanceDifferencesCount slot.

• Threading: False by default. Allows to profit from SMP machines via the Python multiprocessing module.

• nbrCores: controls the maximal number of cores that will be used in the multiprocessing phases. If None is given, the os.cpu_count method is used in order to determine the number of availble cores on the SMP machine.

Warning

If Threading is True, WithConcordanceRelation and WithVetoCounts flags are automatically set both to False.

computeCriterionRelation(c, a, b, hasSymmetricThresholds=True)

Compute the outranking characteristic for actions x and y on criterion c.

computeSingleCriteriaNetflows()

renders the Promethee single criteria netflows matrix M

criterionCharacteristicFunction(c, a, b, hasSymmetricThresholds=True)

Renders the characteristic value of the comparison of a and b on criterion c.

saveSingleCriterionNetflows(fileName='tempnetflows.prn', delimiter=' ', Comments=True)

Delimited save of single criteria netflows matrix

class outrankingDigraphs.CoalitionsOutrankingsFusionDigraph(argPerfTab, coalitionsList=None, actionsSubset=None, CopyPerfTab=True, Comments=False)

With a list of criteria coalitions, a fusion digraph is constructed form the fusion of the corresponding marginal coalitions restricted bipolar outranking digraphs.

When coalitionsList is None, an ‘o-average’ fusion of the decision objectives restricted outranking digraphs is produced (see UnOpposedBipolarOutrankingDigraph class).

class outrankingDigraphs.ConfidentBipolarOutrankingDigraph(argPerfTab=None, distribution='triangular', betaParameter=2, confidence=90.0, coalition=None, hasNoVeto=False, hasBipolarVeto=True, Normalized=True, Debug=False)

Confident bipolar outranking digraph based on multiple criteria of uncertain significance.

The digraph’s bipolar valuation represents the bipolar outranking relation based on a sufficient likelihood of the at least as good as relation that is outranking without veto and counterveto.

By default, each criterion i’ significance weight is supposed to be a triangular random variable of mode w_i in the range 0 to 2*w_i.

Parameters:

• argPerfTab: PerformanceTableau instance or the name (without extension) of a stored one. If None, a random instance is generated.

• distribution: {triangular|uniform|beta}, probability distribution used for generating random weights

• betaParameter: a = b (default = 2)

• confidence: required likelihood (in %) of the outranking relation

• other standard parameters from the BipolarOutrankingDigraph class (see documentation).

computeCLTLikelihoods(distribution='triangular', betaParameter=None, Debug=False)

Renders the pairwise CLT likelihood of the at least as good as relation neglecting all considerable large performance differences polarisations.

showRelationTable(IntegerValues=False, actionsSubset=None, Sorted=True, LikelihoodDenotation=True, hasLatexFormat=False, hasIntegerValuation=False, relation=None, Debug=False)

prints the relation valuation in actions X actions table format.

class outrankingDigraphs.DissimilarityOutrankingDigraph(argPerfTab=None, Debug=False)

Parameters:

performanceTableau (fileName of valid py code)

Specialization of the OutrankingDigraph class for generating temporary dissimilarity random graphs

showAll()

specialize the general showAll method for the dissimilarity case

class outrankingDigraphs.EquiSignificanceMajorityOutrankingDigraph(argPerfTab=None, coalition=None, hasNoVeto=False)

Parameters:

performanceTableau (fileName of valid py code)

Specialization of the general OutrankingDigraph class for temporary outranking digraphs with equisignificant criteria.

class outrankingDigraphs.MultiCriteriaDissimilarityDigraph(perfTab=None, filePerfTab=None)

Parameters:

performanceTableau (fileName of valid py code)

Specialization of the OutrankingDigraph class for generating temporary multiple criteria based dissimilarity graphs.

class outrankingDigraphs.OldRobustOutrankingDigraph(filePerfTab=None, Debug=False, hasNoVeto=True)

Parameters:

performanceTableau (fileName of valid py code)

Specialization of the general OutrankingDigraph class for robustness analysis distinguishing 3 levels of stability.

saveAMPLDataFile(name='temp', Unique=False, Comments=True)

save the ampl reverse data for cplex

saveXMLRubisOutrankingDigraph(name='temp', category='Rubis outranking robustness digraph', subcategory='Choice recommendation', author='digraphs Module (RB)', reference='saved from Python', comment=True, servingD3=True)

save complete robust Rubis problem and result in XML format with unicode encoding.

showRelationTable()

specialisation for integer values

class outrankingDigraphs.OrdinalOutrankingDigraph(argPerfTab=None, coalition=None, hasNoVeto=False)

Parameters:

performanceTableau (fileName of valid py code)

Specialization of the general OutrankingDigraph class for temporary ordinal outranking digraphs

class outrankingDigraphs.OutrankingDigraph(file=None, order=7)

Abstract root class for outranking digraphs inheritating methods both from the generic digraphs.Digraph and from the generic perfTabs.PerformanceTableau root classes. As such, our genuine outranking digraph model is a hybrid object appearing on the one side as digraph with a nodes set (the decision alternatives) and a binary relation (outranking situations) and, on the other side, as a performance tableau with a set of decision alternatives, performance criteria and a table of performance measurements.

Provides common methods to all specialized models of outranking digraphs, the standard outranking digraph model being provided by the outrankingDigraphs.BipolarOutrankingDigraph class.

A given object of this class consists at least in:

1. a potential set of decision actions : an (ordered) dictionary describing the potential decision actions or alternatives with ‘name’ and ‘comment’ attributes,

2. a coherent family of criteria: an (ordered) dictionary of criteria functions used for measuring the performance of each potential decision action with respect to the preference dimension captured by each criterion,

3. the evaluations: a dictionary of performance evaluations for each decision action or alternative on each criterion function.

4. the digraph valuationdomain, a dictionary with three entries: the minimum (-100, means certainly no link), the median (0, means missing information) and the maximum characteristic value (+100, means certainly a link),

5. the outranking relation : a double dictionary defined on the Cartesian product of the set of decision alternatives capturing the credibility of the pairwise outranking situation computed on the basis of the performance differences observed between couples of decision alternatives on the given family if criteria functions.

Warning

Cannot be called directly ! No __init__(self,…) method defined.

computeAMPLData(OldValuation=False)

renders the ampl data list

computeActionsComparisonCorrelations()

renders the comparison correlations between the actions

computeActionsCorrelationDigraph()

renders the pairwise actions comparison digraph

computeCriteriaComparisonCorrelations()

renders the comparison correlations between the criteria

computeCriteriaCorrelationDigraph(ValuedCorrelation=True, WithMedian=False)

renders the ordinal criteria correlation digraph.

computeCriteriaCorrelations(ValuedCorrelation=False)

renders the relation equivalence or correlation between the criteria

computeCriterionCorrelation(criterion, Threading=False, nbrOfCPUs=None, Debug=False, Comments=False)

Renders the ordinal correlation coefficient between the global outranking and the marginal criterion relation.

Uses the digraphs.computeOrdinalCorrelationMP().

Note

Renders a dictionary with the key ‘correlation’ containing the actual bipolar correlation index and the key ‘determination’ containing the minimal determination level D of the self outranking and the marginal criterion relation.

D = sum_{x != y} min(abs(self.relation(x,y)),abs(marginalCriterionRelation(x,y)) / n(n-1)

where n is the number of actions considered.

The correlation index with a completely indeterminate relation is by convention 0.0 at determination level 0.0 .

computeCriterionRelation(c, a, b)

compute the outranking characteristic for actions x and y on criterion c.

computeMarginalCorrelation(args, Threading=False, nbrOfCPUs=None, Debug=False, Comments=False)

Renders the ordinal correlation coefficient between the marginal criterion relation and a given normalized outranking relation.

args = (criterion,relation)

computeMarginalObjectiveCorrelation(args, Threading=False, nbrOfCPUs=None, Debug=False, Comments=False)

Renders the ordinal correlation coefficient between the marginal criterion relation and a given normalized outranking relation.

args = (objective,relation)

computeMarginalObjectivesVersusGlobalRankingCorrelations(ranking, Sorted=True, ValuedCorrelation=False, Threading=False, nbrCores=None, Comments=False)

Method for computing correlations between each individual objective’s outranking relation and the given global ranking relation.

Returns a list of tuples (correlation,objectiveKey) sorted by default in decreasing order of the correlation.

If Threading is True, a multiprocessing Pool class is used with a parallel equivalent of the built-in map function.

If nbrCores is not set, the os.cpu_count() function is used to determine the number of available cores.

Usage example:

>>> from outrankingDigraphs import *
>>> t = Random3ObjectivesPerformanceTableau(
                           numberOfActions=21,
                           numberOfCriteria=17,
                           vetoProbability=0.2,
                           seed=12)
>>> g = BipolarOutrankingDigraph(t)
>>> ranking = g.computeNetFlowsRanking()
>>> g.computeMarginalObjectivesVersusGlobalRankingCorrelations(
                  ranking,Threading=False,Comments=True)
 Marginal objective ordinal correlation with given ranking
 -------------------------------------------------
 Given ranking: ['p04', 'p09', 'p01', 'p08', 'p16', 'p03', 
                 'p13', 'p20', 'p15', 'p10', 'p18', 'p19', 
                 'p06', 'p02', 'p07', 'p11', 'p05', 'p12', 
                 'p14', 'p21', 'p17']
 Objective (weight): correlation
 Soc (135.00):   +0.473
 Eco (135.00):   +0.457
 Env (135.00):   +0.326

computeMarginalVersusGlobalOutrankingCorrelations(Sorted=True, ValuedCorrelation=False, Threading=False, nbrCores=None, Comments=False)

Method for computing correlations between each individual criterion relation with the corresponding global outranking relation.

Returns a list of tuples (correlation,criterionKey) sorted by default in decreasing order of the correlation.

If Threading is True, a multiprocessing Pool class is used with a parallel equivalent of the built-in map function.

If nbrCores is not set, the os.cpu_count() function is used to determine the number of available cores.

computeMarginalVersusGlobalRankingCorrelations(ranking, Sorted=True, ValuedCorrelation=False, Threading=False, nbrCores=None, Comments=False)

Method for computing correlations between each individual criterion relation with the corresponding global ranking relation.

Returns a list of tuples (correlation,criterionKey) sorted by default in decreasing order of the correlation.

If Threading is True, a multiprocessing Pool class is used with a parallel equivalent of the built-in map function.

If nbrCores is not set, the os.cpu_count() function is used to determine the number ofavailable cores.

computeOutrankingConsensusQuality(Sorted=True, ValuedCorrelation=True, Threading=False, nbrCores=None, Comments=False)

Renders the marginal criteria correlations with the corresponding global outranking relation with summary.

computePairwiseComparisons(hasSymmetricThresholds=True)

renders pairwise comparison parameters for all pairs of actions

computePairwiseCompleteComparison(a, b, c)

renders pairwise complete comparison parameters for actions a and b on criterion c.

computePairwiseOddsMatrix()

renders a double dictionary with odds: (positive chaacteristics, negative characteristics) per actions pair.

computeQuantileSortRelation(Debug=False)

Renders the bipolar-valued relation obtained from the self quantile sorting result.

computeSingletonRanking(Comments=False, Debug=False)

Renders the sorted bipolar net determinatation of outrankingness minus outrankedness credibilities of all singleton choices.

res = ((netdet,singleton,dom,absorb)+)

computeVetoesStatistics(level=None)

renders the cut level vetos in dictionary format: vetos = {‘all’: n0, ‘strong: n1, ‘weak’:n2}.

computeVetosShort()

renders the number of vetoes and real vetoes in an OutrankingDigraph.

computeWeightsConcentrationIndex()

Renders the Gini concentration index of the weight distribution

Based on the triangle summation formula.

defaultDiscriminationThresholds(quantile={'ind': 10, 'pref': 20, 'veto': 80, 'weakVeto': 60}, Debug=False, comments=False)

updates the discrimination thresholds with the percentiles from the performance differences.

Parameters:

quantile = {‘ind’: 10, ‘pref’: 20, ‘weakVeto’: 60, ‘veto: 80}.

export3DplotOfActionsCorrelation(plotFileName='actCorr', graphType=None, pictureFormat='pdf', bgcolor='cornsilk', Comments=False)

Using R for producing a plot -pdf format by default- of the principal components of the actions ordinal correlation table.

See export3DplotCriteriaCorrelation()

export3DplotOfCriteriaCorrelation(plotFileName='critCorr', tempDir='.', graphType=None, pictureFormat='pdf', bgcolor='cornsilk', ValuedCorrelation=False, WithMedian=False, Comments=False)

Using R for producing a plot (pdf format by default) of the principal components of the criteria ordinal correlation table.

Parameters:

• plotFileName := name of the created R plot image,

• pictureFormat := ‘png’ (default) | ‘pdf’ | ‘jpeg’ | ‘xfig’,

• graphType := deprecated

• bgcolor := ‘cornsilk’ by default | None,

• ValuedCorrelation := False (tau by default) | True (r(<=>) otherwise,

• WithMedian includes the marginal correlation with the global outranking relation

• tempDir := ‘.’ : default current working directory.

saveActionsCorrelationTable(fileName='tempcorr.prn', delimiter=' ', Bipolar=True, Silent=False, Centered=False)

Delimited save of correlation table

saveCriteriaCorrelationTable(fileName='tempcorr.prn', delimiter=' ', ValuedCorrelation=False, Bipolar=True, Silent=False, Centered=False)

Delimited save of correlation table

saveXMCDA2RubisChoiceRecommendation(fileName='temp', category='Rubis', subcategory='Choice Recommendation', author='digraphs Module (RB)', reference='saved from Python', comment=True, servingD3=False, relationName='Stilde', graphValuationType='bipolar', variant='standard', instanceID='void', stringNA='NA', _OldCoca=True, Debug=False)

save complete Rubis problem and result in XMCDA 2.0 format with unicode encoding.

Warning: obsolete now!

showAll()

specialize the general showAll method with criteria and performance tableau output

showConsiderablePerformancesPolarisation()

prints all considerable performance polarisations.

showCriteriaCorrelationTable(ValuedCorrelation=False, isReturningHTML=False, ndigits=3)

prints the ordinal correlation index tau between criteria in table format.

showCriteriaHierarchy()

shows the Rubis clustering of the ordinal criteria correlation table

showCriterionRelationTable(criterion, actionsSubset=None)

prints the relation valuation in actions X actions table format.

showHTMLPairwiseComparison(a, b, htmlFileName=None)

Exporting the pairwise comparison table of actions a and b in the default system browser. A specific file name may be provided.

showHTMLPairwiseOutrankings(a, b, htmlFileName=None)

Exporting the pairwise outrankings table of actions a and b in the default system browser. A specific file name may be provided.

showMarginalObjectivesVersusGlobalRankingCorrelations(ranking, Sorted=True, ValuedCorrelation=False, Threading=False, nbrCores=None)

Corresponding compute method with Comments = True flag.

showMarginalVersusGlobalOutrankingCorrelation(Sorted=True, ValuedCorrelation=False, Threading=False, nbrOfCPUs=None, Comments=True)

Show method for computeCriterionCorrelation results.

showOldPairwiseComparison(a, b, Debug=False, isReturningHTML=False, hasSymmetricThresholds=True)

Obsolete: Renders the pairwise comprison parameters on all criteria with weak preference and weak veto thresholds.

showOutrankingConsensusQuality(Sorted=True, ValuedCorrelation=True, Threading=False, nbrCores=None, Comments=True)

Show method for the computeOutrankingConsensusQuality() method.

showPairwiseComparison(a, b, Debug=False, isReturningHTML=False, hasSymmetricThresholds=True)

Renders the pairwise comprison parameters on all criteria in html format

showPairwiseComparisonsDistributions()

Renders the lt,leq, eq, geq, gt distributions for all pairs

showPairwiseOutrankings(a, b, Debug=False, isReturningHTML=False, hasSymmetricThresholds=True)

Renders the pairwise outrankings table for actions a and b.

showPerformanceTableau(actionsSubset=None)

Print the performance Tableau.

showPolarisations(cutLevel=None, realVetosOnly=False)

prints all negative and positive polarised situations observed in the OutrankingDigraph instance.

showRelationTable(IntegerValues=False, actionsSubset=None, rankingRule=None, Sorted=False, hasLPDDenotation=False, OddsDenotation=False, StabilityDenotation=False, hasLatexFormat=False, hasIntegerValuation=False, relation=None, ReflexiveTerms=True, fromIndex=None, toIndex=None)

Prints the relation valuation in actions X actions table format. Copeland and NetFlows ranking rule may be applied.

showShort()

specialize the general showShort method with the criteria.

showSingletonRanking(Comments=True, Debug=False)

Calls self.computeSingletonRanking(comments=True,Debug = False). Renders and prints the sorted bipolar net determinatation of outrankingness minus outrankedness credibilities of all singleton choices. res = ((netdet,sigleton,dom,absorb)+)

showVetos(cutLevel=None, realVetosOnly=False)

prints all veto and counter-veto situations observed in the OutrankingDigraph instance.

class outrankingDigraphs.PolarisedOutrankingDigraph(digraph=None, level=None, KeepValues=True, AlphaCut=False, StrictCut=False)

Specilised digraphs.PolarisedDigraph instance for Outranking Digraphs.

Warning

If called with argument digraph=None, a RandomBipolarOutrankingDigraph instance is generated first.

class outrankingDigraphs.RandomBipolarOutrankingDigraph(numberOfActions=7, numberOfCriteria=7, weightDistribution='random', weightScale=[1, 10], commonScale=[0.0, 100.0], commonThresholds=[(10.0, 0.0), (20.0, 0.0), (80.0, 0.0), (80.0, 0.0)], commonMode=('uniform', None, None), hasBipolarVeto=True, Normalized=True, seed=None)

Specialization of the BipolarOutrankingDigraph class for generating temporary Digraphs from RandomPerformanceTableau instances.

Parameters:

See randomPerfTabs.RandomPerformanceTableau class.

class outrankingDigraphs.RandomOutrankingDigraph(numberOfActions=7, numberOfCriteria=7, weightDistribution='random', weightScale=[1, 10], commonScale=[0.0, 100.0], commonThresholds=[(10.0, 0.0), (20.0, 0.0), (80.0, 0.0), (80.0, 0.0)], commonMode=('uniform', None, None), hasBipolarVeto=True, Normalized=True, seed=None)

Dummy for obsolete RandomOutrankingDigraph Class

class outrankingDigraphs.RobustOutrankingDigraph(filePerfTab=None, Debug=False, hasNoVeto=True)

Parameters:

performanceTableau (fileName or valid py code)

Specialization of the general OutrankingDigraph class for new robustness analysis distinguishing between three nested stability levels:

• +4 (resp. -4) : unanimous outranking (resp. outranked;

• +3 (resp. -3) : majority outranking (resp. outranked) situation in all coalitions of equi-ignificant citeria;

• +2 (resp. -2) : validated outranking (resp. outranked) situation with all potential weights compatible with the criteria significance preorder;

• +1 (resp. -1) : validated outranking (resp. outranked) situation with the given criteria significances;

• 0 : indeterminate preferential situation-

Sematics:

• alternative x robustly outranks alternative y when the outranking situation is qualified greater or equal to level +2 and there is no considerable counter-performance observed on a discordant criteria;

• alternative x robustly does not outrank alternative y when the outranking situation is qualified lower or equal to level -2 and there is no considerable performance observed on a discordant criteria.

Usage example:

>>> from outrankingDigraphs import *
>>> t = RandomPerformanceTableau(numberOfActions=7,weightDistribution='random',seed=100)
>>> t.showPerformanceTableau()
 *----  performance tableau -----*
 Criteria |  'g1'    'g2'    'g3'    'g4'    'g5'    'g6'    'g7'   
 Actions  |    4       6       2       7       4       4       2    
 ---------|-------------------------------------------------------
   'a1'   | 44.51   43.90   19.10   16.22   14.81   45.49   41.66  
   'a2'   |   NA    38.75   27.73   21.53   79.70   22.03   12.82  
   'a3'   | 58.00   35.84   41.46   51.16   67.48   33.83   21.92  
   'a4'   | 24.22   29.12   22.41     NA    13.97   31.83   75.74  
   'a5'   | 29.10   34.79   21.52   39.35     NA    69.98   15.45  
   'a6'   | 96.58   62.22   56.90   32.06   80.16   48.80    6.05  
   'a7'   | 82.29   44.23   46.37   47.67   69.62   82.88    9.96  
>>> t.showWeightPreorder()
 *------- weights preordering --------*
 ['g3', 'g7'] (2) <
 ['g1', 'g5', 'g6'] (4) <
 ['g2'] (6) <
 ['g4'] (7)
>>> g = RobustOutrankingDigraph(t)
>>> g
 *------- Object instance description ------*
 Instance class      : RobustOutrankingDigraph
 Instance name       : robust_randomperftab
 Actions             : 7
 Criteria            : 7
 Size                : 19
 Determinateness (%) : 67.53
 Valuation domain    : [-1.00;1.00]
 Attributes          : ['name', 'methodData', 'actions',
                        'order', 'criteria', 'evaluation',
                        'vetos', 'valuationdomain', 'relation',
                        'concordanceRelation',
                        'largePerformanceDifferencesCount',
                        'ordinalRelation', 'equisignificantRelation',
                        'unanimousRelation', 'stability',
                        'gamma', 'notGamma']
>>> g.showRelationTable(StabilityDenotation=True)
 * ---- Relation Table -----
 r/(stab) |  'a1'   'a2'   'a3'   'a4'   'a5'   'a6'   'a7'   
 ---------|------------------------------------------------------------
   'a1'   |    +1.00  -0.03  -0.17  +0.55  +0.00  -0.72  -0.45  
          |   (+4)   (-2)   (-2)   (+2)   (+1)   (-2)   (-2)  
   'a2'   |   +0.03   +1.00  -0.17  +0.21  -0.10  -0.45  -0.45  
          |   (+2)   (+4)   (-2)   (+2)   (-2)   (-2)   (-2)  
   'a3'   |   +0.17  +0.38   +1.00  +0.62  +0.59  +0.00  +0.00  
          |   (+2)   (+2)   (+4)   (+2)   (+2)   (-1)   (-1)  
   'a4'   |   -0.21  -0.21  -0.34   +1.00  -0.21  -0.62  -0.62  
          |   (-2)   (-2)   (-2)   (+4)   (-2)   (-2)   (-2)  
   'a5'   |   +0.03  +0.38  -0.17  +0.48   +1.00  +0.03  -0.72  
          |   (+2)   (+2)   (-2)   (+2)   (+4)   (+2)   (-2)  
   'a6'   |   +0.86  +0.72  +0.00  +0.62  -0.03   +1.00  +0.00  
          |   (+2)   (+2)   (+1)   (+2)   (-2)   (+4)   (+1)  
   'a7'   |   +0.86  +0.52  +0.62  +0.62  +0.72  +0.00   +1.00  
          |   (+2)   (+2)   (+2)   (+2)   (+2)   (-1)   (+4)  

showRelationTable(IntegerValues=False, actionsSubset=None, rankingRule=None, Sorted=True, hasLPDDenotation=False, StabilityDenotation=True, hasLatexFormat=False, hasIntegerValuation=False, relation=None, ReflexiveTerms=True)

prints the relation valuation in actions X actions table format by default with the stability denotation in brackets:

+4 | -4 : unanimous outranking | outranked situation;

+3 | -3 : validated outranking | outranked situation in each coalition of equisignificant criteria;

+2 | -2 : outranking | outranked situation validated with all potential significance weights that are compatible with the given significance preorder;

+1 | -1 : validated outranking | outranked situation with the given significance weights;

0 : indeterminate relational situation.

class outrankingDigraphs.StochasticBipolarOutrankingDigraph(argPerfTab=None, sampleSize=50, samplingSeed=None, distribution='triangular', spread=1.0, likelihood=0.9, coalition=None, hasNoVeto=False, hasBipolarVeto=True, Normalized=False, Debug=False, SeeSampleCounter=False)

Stochastic bipolar outranking digraph based on multiple criteria of uncertain significance.

The digraph’s bipolar valuation represents the median of sampled outranking relations with a sufficient likelihood (default = 90%) to remain positive, repectively negative, over the possible criteria significance ranges.

Each criterion i’ significance weight is supposed to be a triangular random variables of mode w_i in the range 0 to 2*w_i.

Parameters:

• argPerfTab: PerformanceTableau instance or the name of a stored one. If None, a random instance is generated.

• sampleSize: number of random weight vectors used for Monte Carlo simulation.

• distribution: {triangular|extTriangular|uniform|beta(2,2)|beta(4,4)}, probability distribution used for generating random weights

• spread: weight range = weight mode +- (weight mode * spread)

• likelihood: 1.0 - frequency of valuations of opposite sign compared to the median valuation.

• other standard parameters from the BipolarOutrankingDigraph class (see documentation).

computeCDF(x, y, rValue)

computes by interpolation the likelihood of a given rValue with respect to the sampled r(x,y) valuations.

Parameters:

• action key x

• action key y

• r(x,y)

computeCLTLikelihoods(distribution='triangular', Debug=False)

Renders the pairwise CLT likelihood of the at least as good as relation neglecting all considerable large performance differences polarisations.

showRelationStatistics(argument='likelihoods', actionsSubset=None, hasLatexFormat=False, Bipolar=False)

prints the relation statistics in actions X actions table format.

showRelationTable(IntegerValues=False, actionsSubset=None, hasLPDDenotation=False, hasLatexFormat=False, hasIntegerValuation=False, relation=None)

specialising BipolarOutrankingDigraph.showRelationTable() for stochstic instances.

class outrankingDigraphs.SymmetricAverageFusionOutrankingDigraph(argPerfTab, actionsSubset=None, coalition=None, CopyPerfTab=True, Normalized=True, Comments=False)

in development !

class outrankingDigraphs.UnOpposedBipolarOutrankingDigraph(argPerfTab, actionsSubset=None, CopyPerfTab=True, Comments=False)

When operating an o-average fusion of the mariginal outranking digraphs restricted to the coalition of criteria supporting each decision objective, we obtain unopposed outranking situtations, namely validated by one or more decision objectives without being invalidated by any other decision objective.

These positive, as well as negative outranking characteristics, appear hence stable with respect to the importance of the decision objectives when proportional criteria significances are given.

Furthermore, polarising the outranking digraph with considerable performance differences is here restricted to each decision objective, which makes it easier to decide on veto discrimination thresholds.

computeOppositeness(InPercents=False)

Computes the degree in [0.0, 1.0] of oppositeness –preferential disagreement– of the multiple decision objectives.

Renders a dictionary with three entries:

• standardSize : size of the corresponding standard bipolar-valued outranking digraph;

• unopposedSize : size of the the corresponding unopposed bipolar-valued outranking digraph;

• oppositeness : (1.0 - unopposedSize/standardSize); if InPercents has value True, the oppositeness is rendered in percents format.

class outrankingDigraphs.UnanimousOutrankingDigraph(argPerfTab=None, coalition=None, hasNoVeto=False)

Parameters:

performanceTableau (fileName of valid py code)

Specialization of the general OutrankingDigraph class for temporary unanimous outranking digraphs

Back to the Table of Contents

---

2.8. mpOutrankingDigraphs module

Inheritance Diagram

Digraph3 collection of python3 modules for Algorithmic Decision Theory applications.

New Python3.12+ compatible multiprocessing implementation of bipolar-valued outranking digraphs for Linux and MacOS. The potentially unsafe default fork multiprocessing start-method may be either set to ‘spawn’ (default) or to ‘forkserver’. Shared pool given performance tableau must be first saved in the current working directory in a file named ‘sharedPerfTab’.

Copyright (C) 2023 Raymond Bisdorff

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

class mpOutrankingDigraphs.MPBipolarOutrankingDigraph(WithGammaSets=True, Normalized=False, ndigits=4, startMeth='spawn', nbrCores=None)

New variable start-method based MP implementation of the BipolarOutrankingDigraph class.

Parameters:

• Normalized: the valuation domain is set by default to the sum of the criteria weights. If True, the valuation domain is recoded to [-1.0,+1.0].

• ndigits: number of decimal digits of the characteristic valuation, by default set to 4.

• nbrCores: controls the maximal number of cores that will be used in the multiprocessing phases. If None is given, the os.cpu_count() method is used in order to determine the number of available cores on the SMP machine.

• startMethod: ‘spawn’ (default) | ‘forkserver’ | ‘fork’

• The given PerformanceTableau object is shared with the multiprocessing threads via importing a sharedPerfTab.py module stored in the current working directory and containing a saved PerformanceTableau object.

Note

The given PerformanceTableau must be previously saved in the working directory under the name ‘sharedPerfTab’.

Usage example

(11th Gen Intel® Core™ i5-11400 × 12, 16.0 GiB memory, Ubuntu 23.10, Python3.12.0):

>>> from randomPerfTabs import RandomCBPerformanceTableau
>>> pt1 = RandomCBPerformanceTableau(
...         numberOfActions=1000,numberOfCriteria=13,
...         seed=10)
>>> pt1.save('sharedPerfTab')
>>> from mpOutrankingDigraphs import *
>>> bg = MPBipolarOutrankingDigraph(Normalized=True,ndigits=2,
...                                 nbrCores=8,startMeth='spawn')
>>> bg
 *------- Object instance description ------*
 Instance class       : MPBipolarOutrankingDigraph
 Instance name        : rel_sharedPerfTab
 Actions              : 1000
 Criteria             : 13
 Size                 : 517128
 Determinateness (%)  : 66.83
 Valuation domain     : [-1.00;1.00]
 Attributes           : ['name', 'actions', 'order', 'criteria',
                 'objectives', 'NA', 'evaluation', 'nbrThreads',
                 'relation', 'largePerformanceDifferencesCount',
                 'valuationdomain', 'gamma', 'notGamma',
                 'runTimes', 'startMeth']
 ----  Constructor run times (in sec.) ----
 Threads            : 8
 Start method       : 'spawn'
 Total time         : 4.06436
 Data input         : 0.00000
 Compute relation   : 2.79447
 Normalize relation : 0.72327
 Gamma sets         : 0.54659

Warning

When using the forkserver or the spawn multiprocessing start-methods in a python script file, mind that both start-methods re-import into every multiprocessing thread the submitted program file. In order to avoid hence the program script from being recursively executed and producing loads of zombie threads before being killed by the OS, it is compulsory necessary to always explicitely protect the entry point of the main program code with the if __name__ == ‘__main__’: condition. This is not necessary when using instead the classical Unix fork start-method where multiprocessing threads continue in fact the main program code from the point on where they were launched.

showPolarisations()

Prints out all negative and positive polarised outranking situations observed in the MPBipolarOutrankingDigraph instance.

---

2.9. ratingDigraphs module

Inheritance Diagram

Digraph3 collection of python3 modules for Algorithmic Decision Theory applications.

Module for relative and absolute rating of multicriteria performance records with abstract RatingDigraph root class.

The module, better suitable for rating problems of small sizes (< 500 mulicriteria performance records), reimplements a simpler and more consistent version of the MP optimised QuantilesSortingDigraph and the LearnedQuantilesRatingDigraph classes from the sortingDigraphs module.

Copyright (C) 2016-2023 Raymond Bisdorff.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR ANY PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

Note

The actions attribute of RatingDigraph instances contains besides the standard Digraph.actions (stored in self.actionsOrig) also the quantile limit profiles (stored in self.profiles).

The ratingDigraphs module is not optimised for BigData applications. In such cases, it is recommended to use instead the MP optimised sortingDigraph module.

class ratingDigraphs.RatingByLearnedQuantilesDigraph(argPerfQuantiles=None, newData=None, quantiles=None, rankingRule='NetFlows', outrankingModel='standard', distribution='triangular', betaParameter=2, confidence=90.0, Threading=False, nbrCores=None, CopyPerfTab=True, Debug=False)

Constructor for a learned quantiles rating-by sorting and rating-by-ranking digraph. See the sortingDigraphs.LearnedQuantilesRatingDigraph class.

Parameters

argPerfQuantiles: valid stored PerformanceQuantiles instance,

newData: new random actions or performance tableau generated with the RandomPerformanceGenerator class,

quantiles: integer number of quantile classes,

LowerClosed: {True | False (default upper closed quantiles)},

rankingRule: ‘NetFlows’ (default).

outrankingModel: {‘standard’ (default) | ‘confident’ | ‘robust’},

Parameters for the confident outranking model:

distribution: {‘triangular’ (default)| ‘uniform’ | ‘beta’},

betaParameter : 2 (default),

confidence: alpha% confidence level (in percents, 90.0 default).

Example usage:

>>> # generating random historical performance records and quantiles
>>> from randomPerfTabs import RandomPerformanceTableau
>>> hpt = RandomPerformanceTableau(numberOfActions=1000,seed=1)
>>> from performanceQuantiles import PerformanceQuantiles
>>> pq = PerformanceQuantiles(hpt,numberOfBins=7,LowerClosed=True,Debug=False)
>>> # generating new incoming performance records of the same kind
>>> from randomPerfTabs import RandomPerformanceGenerator
>>> tpg = RandomPerformanceGenerator(hpt,instanceCounter=0,seed=1)
>>> newRecords = tpg.randomActions(10)
>>> # updating the historical performance quantiles
>>> pq.updateQuantiles(newRecords,historySize=None)
>>> # rating the new set of performance records after
>>> from ratingDigraphs import RatingByLearnedQuantilesDigraph
>>> lqr = RatingByLearnedQuantilesDigraph(pq,newRecords,Debug=False)
>>> lqr.showRatingByQuantilesSorting(strategy='average')
    *---- rating by quantiles sorting result----*
    [0.86-<[ : ['a06']
    [0.71-0.86[ : ['a04']
    [0.57-0.71[ : ['a07']
    [0.43-0.57[ : ['a03', 'a05', 'a08']
    [0.29-0.43[ : ['a02', 'a09']
    [0.14-0.29[ : ['a01', 'a10']
>>> lqr.showRatingByQuantilesRanking(Descending=True)
    *-------- rating by quantiles ranking result ---------
    [0.57 - 0.71[ ['a06']
    [0.43 - 0.57[ ['a07', 'a04', 'a05', 'a09']
    [0.29 - 0.43[ ['a08', 'a03', 'a02', 'a01']
    [0.14 - 0.29[ ['a10']

class ratingDigraphs.RatingByRelativeQuantilesDigraph(argPerfTab, quantiles=None, LowerClosed=False, outrankingModel='standard', distribution='triangular', betaParameter=2, confidence=90.0, rankingRule='NetFlows', Threading=False, nbrCores=None, CopyPerfTab=True, Debug=False)

Constructor for a relative quantiles rating-by sorting and rating-by-ranking digraph. See the sortingDigraphs.QuantilesSortingDigraph class.

Parameters

argPerfTab: valid stored PerformanceTableau instance,

quantiles: integer number of quantile classes,

LowerClosed: {True | False (default upper closed quantiles)},

rankingRule: ‘NetFlows’ (default).

outrankingModel: {‘standard’ (default) | ‘confident’ | ‘robust’ | ‘mp’ },

Parameters for the confident outranking model:

distribution: {‘triangular’ (default)| ‘uniform’ | ‘beta’},

betaParameter : 2 (default),

confidence: alpha% confidence level (in percents, 90.0 default).

Example usage:

>>> # generating random multicriteria performance records
>>> from randomPerfTabs import RandomPerformanceTableau
>>> pt = RandomPerformanceTableau(numberOfActions=50,seed=3)
>>> # rating-by-sorting with relative quantiles
>>> from ratingDigraphs import RatingByRelativeQuantilesDigraph
>>> g = RatingByRelativeQuantilesDigraph(pt,7,LowerClosed=True)
>>> g.showRatingByQuantileSorting(strategy='average')
    *---- rating by quantiles sorting result----*
    [0.71-<[ : ['a07']
    [0.71-0.86[ : ['a08', 'a48']
    [0.57-0.71[ : ['a04', 'a06', 'a09', 'a12', 'a19', 'a23',
                   'a27', 'a33', 'a38', 'a39', 'a43']
    [0.43-0.71[ : ['a11', 'a18']
    [0.43-0.57[ : ['a03', 'a20', 'a22', 'a29', 'a30', 'a31',
                   'a41', 'a47', 'a49']
    [0.29-0.57[ : ['a01', 'a26', 'a46', 'a50']
    [0.29-0.43[ : ['a05', 'a10', 'a13', 'a16', 'a17', 'a21',
                   'a28', 'a32', 'a37']
    [0.14-0.43[ : ['a40']
    [0.14-0.29[ : ['a15', 'a24', 'a25', 'a34', 'a35', 'a36',
                   'a42', 'a44', 'a45']
    [0.00-0.29[ : ['a14']
    [0.00-0.14[ : ['a02']
>>> g.showRatingByQuantilesRanking()
    *-------- rating by quantiles ranking result ---------
    [0.57 - 0.71[ ['a48', 'a23', 'a07']
    [0.43 - 0.57[ ['a04', 'a27', 'a33', 'a38', 'a09', 'a08',
                   'a41', 'a11', 'a06', 'a46', 'a19', 'a47',
                   'a49', 'a39', 'a43', 'a12', 'a22', 'a20',
                   'a32']
    [0.29 - 0.43[ ['a01', 'a18', 'a17', 'a37', 'a16', 'a30',
                   'a31', 'a21', 'a50', 'a05', 'a29', 'a02',
                   'a13', 'a26', 'a40']
    [0.14 - 0.29[ ['a03', 'a42', 'a28', 'a10', 'a36', 'a45',
                   'a44', 'a34', 'a25', 'a24', 'a35', 'a14',
                   'a15']

class ratingDigraphs.RatingDigraph

Abstract root class with generic private and public methods

exportRatingByRankingGraphViz(fileName=None, Comments=True, graphType='png', graphSize='7,7', fontSize=10, bgcolor='cornsilk', Debug=False)

export GraphViz dot file for Hasse diagram drawing filtering.

exportRatingBySortingGraphViz(fileName=None, direction='decreasing', Comments=True, graphType='png', bgcolor='cornsilk', graphSize='7,7', fontSize=10, relation=None, Debug=False)

export GraphViz dot file for weak order (Hasse diagram) drawing filtering from SortingDigraph instances.

showAllQuantiles()

prints the performance quantiles tableau in the session console.

showCriteriaQuantileLimits(ByCriterion=False)

Shows category minimum and maximum limits for each criterion.

showHTMLPerformanceHeatmap()

shows the html heatmap version of the performance tableau in a browser window (see perfTabs.htmlPerformanceHeatMap() method ).

Parameters:

• actionsList and criteriaList, if provided, give the possibility to show the decision alternatives, resp. criteria, in a given ordering.

• WithActionNames = True (default False) will show the action names instead of the short names or the identifyers.

• ndigits = 0 may be used to show integer evaluation values.

• colorLevels may be 3, 5, 7, or 9.

• When no actionsList is provided, the decision actions are ordered from the best to the worst. This ranking is obtained by default with the Copeland rule applied on a standard BipolarOutrankingDigraph.

• When the SparseModel flag is put to True, a sparse PreRankedOutrankingDigraph construction is used instead.

• the outrankingModel parameter (default = ‘standard’) allows to switch to alternative BipolarOutrankingDigraph constructors, like ‘confident’ or ‘robust’ models. When called from a bipolar-valued outrankingDigraph instance, outrankingModel = ‘this’ keeps the current outranking model without recomputing by default the standard outranking model.

• The minimalComponentSize allows to control the fill rate of the pre-ranked model. When minimalComponentSize = n (the number of decision actions) both the pre-ranked model will be in fact equivalent to the standard model.

• rankingRule = ‘NetFlows’ (default) | ‘Copeland’ | ‘Kohler’ | ‘RankedPairs’ | ‘ArrowRaymond’ | ‘IteratedNetFlows’ | ‘IteraredCopeland’. See tutorial on ranking mith multiple incommensurable criteria.

• when the StoreRanking flag is set to True, the ranking result is storted in self.

• Quantiles used for the pre-ranked decomposition are put by default to n (the number of decision alternatives) for n < 50. For larger cardinalities up to 1000, quantiles = n /10. For bigger performance tableaux the quantiles parameter may be set to a much lower value not exceeding usually 10.

• The pre-ranking may be obtained with three ordering strategies for the quantiles equivalence classes: ‘average’ (default), ‘optimistic’ or ‘pessimistic’.

• With Correlations = True and criteriaList = None, the criteria will be presented from left to right in decreasing order of the correlations between the marginal criterion based ranking and the global ranking used for presenting the decision alternatives.

• For large performance Tableaux, multiprocessing techniques may be used by setting Threading = True in order to speed up the computations; especially when Correlations = True.

• By default, the number of cores available, will be detected. It may be necessary in a HPC context to indicate the exact number of singled threaded cores in fact allocated to the multiprocessing job.

>>> from randomPerfTabs import RandomPerformanceTableau
>>> rt = RandomPerformanceTableau(seed=100)
>>> rt.showHTMLPerformanceHeatmap(colorLevels=5,Correlations=True)

showHTMLRatingByQuantileSorting(title='Quantiles Preordering', Descending=True, strategy='average', htmlFileName=None)

Shows the html version of the quantile preordering in a browser window.

The ordring strategy is either:

• average (default), following the averag of the upper and lower quantile limits,

• optimistic, following the upper quantile limits (default),

• pessimistic, following the lower quantile limits.

showHTMLRatingHeatmap(WithActionNames=False, colorLevels=7, pageTitle=None, ndigits=2, rankingRule=None, Correlations=False, Threading=False, nbrOfCPUs=None, Debug=False, htmlFileName=None)

Specialisation of html heatmap version showing the performance tableau in a browser window; see perfTabs.showHTMLPerformanceHeatMap() method.

Parameters:

• ndigits = 0 may be used to show integer evaluation values.

• If no actionsList is provided, the decision actions are ordered from the best to the worst following the ranking of the LearnedQuatilesRatingDigraph instance.

• It may interesting in some cases to use RankingRule = ‘NetFlows’.

• With Correlations = True and criteriaList = None, the criteria will be presented from left to right in decreasing order of the correlations between the marginal criterion based ranking and the global ranking used for presenting the decision alternatives.

• Computing the marginal correlations may be boosted with Threading = True, if multiple parallel computing cores are available.

showHTMLSorting(Reverse=True, htmlFileName=None)

shows the html version of the sorting result in a browser window.

showRatingByQuantilesRanking(Descending=True, Debug=False)

Show rating-by-ranking result.

showRatingByQuantilesSorting(strategy='average')

Dummy show method for the commenting _computeQuantileOrdering() method.

showSorting(Reverse=True, isReturningHTML=False, Debug=False)

Shows sorting results in decreasing or increasing (Reverse=False) order of the categories. If isReturningHTML is True (default = False) the method returns a htlm table with the sorting result.

showSortingCharacteristics(action=None)

Renders a bipolar-valued bi-dictionary relation representing the degree of credibility of the assertion that “action x in A belongs to category c in C”, ie x outranks low category limit and does not outrank the high category limit.

Back to the Table of Contents

---

2.10. sortingDigraphs module

A tutorial with coding examples for solving multi-criteria rating problems is available here: Rating into relative performance quantiles

Inheritance Diagram

Digraph3 collection of python3 modules for Algorithmic Decision Theory applications.

Module for sorting and rating applications.

Copyright (C) 2016-2023 Raymond Bisdorff.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR ANY PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.

class sortingDigraphs.ConfidentQuantilesSortingDigraph(argPerfTab=None, limitingQuantiles=None, LowerClosed=False, PrefThresholds=True, hasNoVeto=False, outrankingType='confident', distribution='triangular', betaParameter=2, confidence=90.0, WithSortingRelation=True, StoreSorting=False, CopyPerfTab=False, Comments=False, Debug=False)

Specialisation of the root QuantilesSortingDigraph class for sorting of a large set of alternatives into confident quantiles delimited ordered classes.

Note

The constructor requires a valid PerformanceTableau instance. If no number of limiting quantiles is given, then a default profile with the limiting quartiles Q0,Q1,Q2, Q3 and Q4 is used on each criteria. By default upper closed limits of categories are supposed to be used in the sorting.

Example Python3 session:

>>> from sortingDigraphs import ConfidentQuantilesSortingDigraph
>>> from randomPerfTabs import RandomCBPerformanceTableau
>>> t = RandomCBPerformanceTableau(numberOfActions=7,numberOfCriteria=5,
...                                weightDistribution='equiobjectives')
>>> cqs = ConfidentQuantilesSortingDigraph(t,limitingQuantiles=7)
>>> cqs.showSorting()
*--- Sorting results in descending order ---*
]0.86 - 1.00]:       []
]0.71 - 0.86]:       ['a03']
]0.57 - 0.71]:       ['a04']
]0.43 - 0.57]:       ['a04', 'a05', 'a06']
]0.29 - 0.43]:       ['a01', 'a02', 'a06', 'a07']
]0.14 - 0.29]:       []
]< - 0.14]:          []
>>> cqs.showQuantileOrdering()
]0.71-0.86] : ['a03']
]0.43-0.71] : ['a04']
]0.43-0.57] : ['a05']
]0.29-0.57] : ['a06']
]0.29-0.43] : ['a07', 'a02', 'a01']

class sortingDigraphs.LearnedQuantilesRatingDigraph(argPerfQuantiles=None, newData=None, quantiles=None, hasNoVeto=False, valuationScale=(-1, 1), rankingRule='NetFlows', WithSorting=True, Threading=False, tempDir=None, nbrOfCPUs=None, Comments=False, Debug=False)

Specialisation of the root sortingDigraphs.SortingDigraph class for absolute rating of a new set of decision actions with normed performance quantiles gathered from historical data.

Note

The constructor requires a valid performanceQuantiles.PerformanceQuantiles instance.

Example Python session:

>>> from sortingDigraphs import *
>>> # historical data
>>> from randomPerfTabs import RandomCBPerformanceTableau
>>> nbrActions=1000
>>> nbrCrit = 13
>>> seed = 100
>>> tp = RandomCBPerformanceTableau(numberOfActions=nbrActions,numberOfCriteria=nbrCrit,seed=seed)
>>> pq = PerformanceQuantiles(tp,numberOfBins='deciles',LowerClosed=True,Debug=False)
>>> # new incoming decision actions of the same kind
>>> from randomPerfTabs import RandomPerformanceGenerator as PerfTabGenerator
>>> tpg = PerfTabGenerator(tp,instanceCounter=0,seed=seed)
>>> newActions = tpg.randomActions(10)
>>> # rating the new set of decision actions after
>>> # updating the historical performance quantiles
>>> pq.updateQuantiles(newActions,historySize=None)
>>> nqr = LearnedQuantilesRatingDigraph(pq,newActions)
>>> # inspecting the rating result
>>> nqr.showQuantilesRating()
*-------- Learned quantiles rating result ---------
[0.60 - 0.70[ ['a01']
[0.50 - 0.60[ ['a07', 'a10', 'a02', 'a08', 'a09']
[0.40 - 0.50[ ['a03', 'a06', 'a05']
[0.30 - 0.40[ ['a04']
>>> nqr.showHTMLRatingHeatmap(pageTitle='Heatmap of Quantiles Rating')

computeCategoryContents(Debug=False)

Computes the quantiles sorting results per quantile category.

computeQuantileOrdering(strategy=None, Descending=True, HTML=False, Comments=False, Debug=False)

Orders the quantiles sorting result of self.newActions.

Parameters:

• Descending: listing in decreasing (default) or increasing quantile order.

• strategy: ordering in an {‘optimistic’ (default) | ‘pessimistic’ | ‘average’} in the uppest, the lowest or the average potential quantile.

computeQuantilesRating(Debug=False)

Renders an ordered dictionary of non empty quantiles in ascending order.

computeRatingRelation(Debug=False, StoreRating=True)

Computes a bipolar rating relation using a pre-ranking (list of lists) of the self-actions (self.newActions + self.profiles).

computeSortingCharacteristics(action=None, Debug=False)

Renders a bipolar-valued bi-dictionary relation (newActions x profiles) representing the degree of credibility of the assertion that “action x in A belongs to quantile category c profiles”, If LowerClosed is True, x outranks the category low limit and x does not outrank the category high limit, or If LowerClosed is False, ie UPPERCLosed is True, the category low limit does not outrank x and the category high limit does outrank x.

exportRatingByRankingGraphViz(fileName=None, Comments=True, graphType='png', graphSize='7,7', fontSize=10, bgcolor='cornsilk', Debug=False)

export GraphViz dot file for Hasse diagram drawing filtering.

exportRatingBySortingGraphViz(fileName=None, Comments=True, graphType='png', graphSize='12,12', fontSize=10, bgcolor='cornsilk')

Graphviz drawing of the rating-by-sorting digraph

exportRatingGraphViz(fileName=None, Comments=True, graphType='png', graphSize='7,7', fontSize=10, bgcolor='cornsilk')

Dummy for self.exportRatingByRankingGraphViz()

showActionCategories(action, Debug=False, Comments=True)

Renders the union of categories in which the given action is sorted positively or null into. Returns a tuple : action, lowest category key, highest category key, membership credibility !

showActionsSortingResult(actionsSubset=None, Debug=False)

Shows the quantiles sorting result of all (default) or a subset of the decision actions.

showHTMLPerformanceHeatmap()

shows the html heatmap version of the performance tableau in a browser window (see perfTabs.htmlPerformanceHeatMap() method ).

Parameters:

• actionsList and criteriaList, if provided, give the possibility to show the decision alternatives, resp. criteria, in a given ordering.

• WithActionNames = True (default False) will show the action names instead of the short names or the identifyers.

• ndigits = 0 may be used to show integer evaluation values.

• colorLevels may be 3, 5, 7, or 9.

• When no actionsList is provided, the decision actions are ordered from the best to the worst. This ranking is obtained by default with the Copeland rule applied on a standard BipolarOutrankingDigraph.

• When the SparseModel flag is put to True, a sparse PreRankedOutrankingDigraph construction is used instead.

• the outrankingModel parameter (default = ‘standard’) allows to switch to alternative BipolarOutrankingDigraph constructors, like ‘confident’ or ‘robust’ models. When called from a bipolar-valued outrankingDigraph instance, outrankingModel = ‘this’ keeps the current outranking model without recomputing by default the standard outranking model.

• The minimalComponentSize allows to control the fill rate of the pre-ranked model. When minimalComponentSize = n (the number of decision actions) both the pre-ranked model will be in fact equivalent to the standard model.

• rankingRule = ‘NetFlows’ (default) | ‘Copeland’ | ‘Kohler’ | ‘RankedPairs’ | ‘ArrowRaymond’ | ‘IteratedNetFlows’ | ‘IteraredCopeland’. See tutorial on ranking mith multiple incommensurable criteria.

• when the StoreRanking flag is set to True, the ranking result is storted in self.

• Quantiles used for the pre-ranked decomposition are put by default to n (the number of decision alternatives) for n < 50. For larger cardinalities up to 1000, quantiles = n /10. For bigger performance tableaux the quantiles parameter may be set to a much lower value not exceeding usually 10.

• The pre-ranking may be obtained with three ordering strategies for the quantiles equivalence classes: ‘average’ (default), ‘optimistic’ or ‘pessimistic’.

• With Correlations = True and criteriaList = None, the criteria will be presented from left to right in decreasing order of the correlations between the marginal criterion based ranking and the global ranking used for presenting the decision alternatives.

• For large performance Tableaux, multiprocessing techniques may be used by setting Threading = True in order to speed up the computations; especially when Correlations = True.

• By default, the number of cores available, will be detected. It may be necessary in a HPC context to indicate the exact number of singled threaded cores in fact allocated to the multiprocessing job.

>>> from randomPerfTabs import RandomPerformanceTableau
>>> rt = RandomPerformanceTableau(seed=100)
>>> rt.showHTMLPerformanceHeatmap(colorLevels=5,Correlations=True)

showHTMLQuantilesSorting(Descending=True, strategy='average', htmlFileName=None)

Shows the html version of the quantile sorting result in a browser window.

The ordring strategy is either:

• optimistic, following the upper quantile limits (default),

• pessimistic, following the lower quantile limits,

• average, following the averag of the upper and lower quantile limits.

showHTMLRatingHeatmap(actionsList=None, WithActionNames=False, criteriaList=None, colorLevels=7, pageTitle=None, ndigits=2, rankingRule=None, Correlations=False, Threading=False, nbrOfCPUs=None, Debug=False, htmlFileName=None)

Specialisation of html heatmap version showing the performance tableau in a browser window; see perfTabs.showHTMLPerformanceHeatMap() method.

Parameters:

• actionsList and criteriaList, if provided, give the possibility to show the decision alternatives, resp. criteria, in a given ordering.

• ndigits = 0 may be used to show integer evaluation values.

• If no actionsList is provided, the decision actions are ordered from the best to the worst following the ranking of the LearnedQuatilesRatingDigraph instance.

• It may interesting in some cases to use RankingRule = ‘NetFlows’.

• With Correlations = True and criteriaList = None, the criteria will be presented from left to right in decreasing order of the correlations between the marginal criterion based ranking and the global ranking used for presenting the decision alternatives.

• Computing the marginal correlations may be boosted with Threading = True, if multiple parallel computing cores are available.

Suppose we observe the following rating result:

>>> nqr.showQuantilesRating()
[0.50 - 0.75[ ['a1005', 'a1010', 'a1008', 'a1002', 'a1006']
[0.25 - 0.50[ ['a1003', 'a1001', 'a1007', 'a1004', 'a1009']
>>> nqr.showHTMLRatingHeatmap(pageTitle='Heat map of the ratings',
...                           Correlations=True,
...                           colorLevels = 5)

showOrderedRelationTable(relation=None, direction='decreasing')

Showing the relation table in decreasing (default) or increasing order.

showQuantilesSorting(strategy='average')

Dummy show method for the commenting computeQuantileOrdering() method.

showRankingScores(direction='descending')

Shows the ranking scores of the Copeland or the netflows ranking rule, the number of incoming arcs minus the number of outgoing arcs, resp. the sum of inflows minus the outflows.

class sortingDigraphs.NormedQuantilesRatingDigraph(argPerfQuantiles=None, newData=None, quantiles=None, hasNoVeto=False, valuationScale=(-1, 1), rankingRule='NetFlows', WithSorting=True, Threading=False, tempDir=None, nbrOfCPUs=None, Comments=False, Debug=False)

Obsolete name for backward compatibility

class sortingDigraphs.QuantilesSortingDigraph(argPerfTab=None, limitingQuantiles=None, LowerClosed=False, PrefThresholds=True, hasNoVeto=False, outrankingType='bipolar', WithSortingRelation=True, CompleteOutranking=False, StoreSorting=False, CopyPerfTab=False, Threading=False, tempDir=None, nbrCores=None, nbrOfProcesses=None, Comments=False, Debug=False)

Specialisation of the root sortingDigraphs.SortingDigraph class for sorting of a large set of alternatives into quantiles delimited ordered classes.

Note

The constructor requires a valid PerformanceTableau instance. If no number of limiting quantiles is given, then a default profile with the limiting quartiles Q0,Q1,Q2, Q3 and Q4 is used on each criteria. By default upper closed limits of categories are supposed to be used in the sorting.

Example Python3 session:

>>> from sortingDigraphs import QuantilesSortingDigraph
>>> from randomPerfTabs import RandomCBPerformanceTableau
>>> t = RandomCBPerformanceTableau(numberOfActions=7,numberOfCriteria=5,
...                                weightDistribution='equiobjectives')
>>> qs = QuantilesSortingDigraph(t,limitingQuantiles=7)
>>> qs.showSorting()
*--- Sorting results in descending order ---*
]0.86 - 1.00]:       []
]0.71 - 0.86]:       ['a03']
]0.57 - 0.71]:       ['a04']
]0.43 - 0.57]:       ['a04', 'a05', 'a06']
]0.29 - 0.43]:       ['a01', 'a02', 'a06', 'a07']
]0.14 - 0.29]:       []
]< - 0.14]:          []
>>> qs.showQuantileOrdering()
]0.71-0.86] : ['a03']
]0.43-0.71] : ['a04']
]0.43-0.57] : ['a05']
]0.29-0.57] : ['a06']
]0.29-0.43] : ['a07', 'a02', 'a01']
>>> qs.exportGraphViz('quantilesSorting')

computeCategoryContents(Reverse=False, Comments=False, StoreSorting=True, Threading=False, nbrOfCPUs=None)

Computes the sorting results per category.

computeQuantileOrdering(strategy='average', Descending=True, HTML=False, title='Quantiles Preordering', Comments=False, Debug=False)

Parameters:

• Descending: listing in decreasing (default) or increasing quantile order.

• strategy: ordering in an {‘optimistic’ | ‘pessimistic’ | ‘average’ (default)} in the uppest, the lowest or the average potential quantile.

computeSortingCharacteristics(action=None, Comments=False, StoreSorting=False, Debug=False, Threading=False, nbrOfCPUs=None)

Renders a bipolar-valued bi-dictionary relation representing the degree of credibility of the assertion that “action x in A belongs to category c in C”, ie x outranks low category limit and does not outrank the high category limit.

computeSortingRelation(categoryContents=None, Debug=False, StoreSorting=True, Threading=False, nbrOfCPUs=None, Comments=False)

constructs a bipolar sorting relation using the category contents.

computeWeakOrder(Descending=True, Debug=False)

Specialisation for QuantilesSortingDigraphs.

getActionsKeys(action=None, withoutProfiles=True)

extract normal actions keys()

showActionCategories(action, Debug=False, Comments=True, Threading=False, nbrOfCPUs=None)

Renders the union of categories in which the given action is sorted positively or null into. Returns a tuple : action, lowest category key, highest category key, membership credibility !

showActionsSortingResult(actionSubset=None, Debug=False)

shows the quantiles sorting result all (default) of a subset of the decision actions.

showCriteriaCategoryLimits(ByCriterion=False)

Dummy for showCriteriaQuantileLimits()

showCriteriaQuantileLimits(ByCriterion=False)

Shows category minimum and maximum limits for each criterion.

showHTMLQuantileOrdering(title='Quantiles Preordering', Descending=True, strategy='average', htmlFileName=None)

Shows the html version of the quantile preordering in a browser window.

The ordring strategy is either:

• average (default), following