.. meta:: :description: Documentation of the Digraph3 collection of python3 modules for algorithmic decision theory :keywords: Algorithmic Decision Theory, Outranking Digraphs, MIS and kernels, Multiple Criteria Decision Aid, Bipolar-valued Epistemic Logic .. |location_link1| raw:: html https://digraph3.readthedocs.io/en/latest/ .. |location_link3| raw:: html © .. |location_link4| raw:: html Algorithmic Decision Theory Python resources for Algorithmic Decision Theory ================================================ Wecome! This is the documentation for the **Digraph3** *Python* programming resources. :Author: Raymond Bisdorff, Emeritus Professor of Applied Mathematics and Computer Science, University of Luxdembourg :Url: https://rbisdorff.github.io/ :Version: |version| (release: |release|) :Copyright: R. Bisdorff |location_link3| 2013-2024 .. image:: introDoc2.png :width: 500pt :align: center .. toctree:: :hidden: :numbered: :maxdepth: 2 tutorial techDoc pearls adtLectures compStatLectures digraph3Archives errataList .. _Documents: Parts of the documentation .......................... :New: - A series of tutorials for tackling large and big outranking digraphs: see :ref:`BigDigraphs-Tutorial-label` - A :py:mod:`pairings` module for solving pairing problems illustrated with two tutorials on computing **fair** :ref:`intergroup` and :ref:`intragroup` pairing solutions #. `Tutorials `_ .. raw:: html Start here #. `Reference manual `_ .. raw:: html Technical documentation and source code of all Digraph3 modules #. `Pearls of bipolar-valued epistemic logic `_ .. raw:: html Advanced theoretical and computational topics #. `Digraph3 Book `_ .. raw:: html Springer ISOR 324 Book cover
Example files (zip archive, 236.4kB)
Errata List #. `Algorithimc Decision Theory Lectures `_ .. raw:: html 2x2 reduced copies of the presentation slides #. `Computational Statistics Lectures `_ .. raw:: html 2x2 reduced copies of the presentation slides #. `Archives `_ .. raw:: html Historical case studies and example graphs **Indices and search results** #. `General Index `_ .. raw:: html All classes, functions and terms #. `Module Index `_ .. raw:: html Quick access to all the Digraph3 modules #. `Search page `_ .. raw:: html Results of current search request .. role:: raw-html(raw) :format: html .. _Introduction-label: Introduction ............ | *This documentation is dedicated to* | *our colleague and dear friend* | *the late Prof.* Marc ROUBENS The *Digraph3 documentation*, available on the `Read The Docs `_ site: |location_link1|, describes the Python3 resources for implementing decision algorithms via **bipolar-valued outranking** digraphs [:raw-html:`1`]. These computing resources are useful in the field of `Algorithmic Decision Theory `_ and more specifically in the field of **Multiple-Criteria Decision Aiding** [:raw-html:`2`]. They provide practical tools for a Master Course on |location_link4| taught at the University of Luxembourg. The documentation contains, first, a set of tutorials introducing the main objects like **digraphs**, **outranking digraphs** and **performance tableaux**. There is also a tutorial provided on **undirected graphs**. Some tutorials are problem oriented and show how to compute the **winner of an election**, how to build a **best choice recommendation**, or **how to linearly rank or rate** with multiple incommensurable performance criteria. The tutorial about **split**, **interval** and **permutation graphs** is inspired by *Martin Golumbic* 's book on *Algorithmic Graph Theory and Perfect Graphs* [:raw-html:`3`]. We also provide a tutorial on **tree graphs** and **spanning forests**. Recently added, the reader may find two tutorials on **fairly** solving **inter**-, respectively **intragroup pairing** problems. The second Section concerns the **extensive reference manual** of the collection of provided Python3 modules, classes and methods. The main classes in this collection are the :py:class:`digraphs.Digraph` overall root class, the :py:class:`perfTabs.PerformanceTableau` class and the :py:class:`outrankingDigraphs.BipolarOutrankingDigraph` class. The technical documentation also provides insight into the complete source code of all modules, classes and methods. The third Section exhibits some pearls of **bipolar-valued epistemic logic** that enrich the Digraph3 resources. These short topics illustrate well the very computational benefit one may get when working in a bipolar-valued logical framework. And, more specifically, the essential part the *logically neutral* **undeterminate** value is judiciously playing therein. The fourth and fifth sections provide 2x2-reduced notes of the author's lectures on **Algorithmic Decision Theory** and **Computational Statistics** given at the University of Luxembourg in Autumn 2019 and Spring 2020. The last section gathers **historical case studies** with example digraphs compiled before 2006 and concerning the early development of tools and methods for enumerating *non isomorphic maximal independent sets* in undirected graphs and computing *digraph kernels*. .. _Bibliography-label: .. **References** .. raw:: html

References

[1]

Bisdorff (Feb 2022). Algorithmic Decision Making with Python Resources: From multicriteria performance records to decision algorithms via bipolar-valued outranking digraphs. Springer Verlag Heidelberg, International Series in Operations Research & Management Science ISOR 324, ISBN 978-3-030-90927-2, xli, 346 pages (see https://doi.org/10.1007/978-3-030-90928-4).

[2]

Bisdorff, L.C. Dias, P. Meyer, V. Mousseau and M. Pirlot (Eds.) (2015). Evaluation and decision models with multiple criteria: Case studies. Springer-Verlag Berlin Heidelberg, International Handbooks on Information Systems, ISBN 978-3-662-46815-9, 643 pages.

[3]

Ch. Golumbic (2004), Algorithmic Graph Theory and Perfect Graphs 2nd Ed., Annals of Discrete Mathematics 57, Elsevier.

.. .. [BISD-22i] R. Bisdorff (Feb 2022). *Algorithmic Decision Making with Python Resources: From multicriteria performance records to decision algorithms via bipolar-valued outranking digraphs*. Springer Verlag Heidelberg, International Series in Operations Research & Management Science ISOR 324, ISBN 978-3-030-90927-2, xli, 346 pages (see https://doi.org/10.1007/978-3-030-90928-4). .. .. [BISD-15i] R. Bisdorff, L.C. Dias, P. Meyer, V. Mousseau and M. Pirlot (Eds.) (2015). *Evaluation and decision models with multiple criteria: Case studies*. Springer-Verlag Berlin Heidelberg, International Handbooks on Information Systems, `ISBN 978-3-662-46815-9 `_, 643 pages. .. .. [GOLU-04i] M. Ch. Golumbic (2004), *Agorithmic Graph Theory and Perfect Graphs* 2nd Ed., Annals of Discrete Mathematics 57, Elsevier.