Digraph3 Data sets

The following pages gather historical case studies and examples concerning the active development of the Digraph3 collection of python3 modules for implementing tools and methods of the RuBis decision aiding approach [1].

Enumerating non isomorphic kernels in symmetric digraphs

List of case studies and examples of kernel orbits

• St-Niclas graphs
• Enumerating non isomorphic kernels in cycle graphs
• The Petersen graph
• The Coxeter graph
• The Tutte-Coxeter graph
• The Franklin graph
• The Heawood graph
• The Chvátal graph

Computing best choice recommendations

Best unique choice problem statement

• Perny's classic car selection problem (1992)
• Well known postal parcels triage machine selection (Roy, Bouyssou 1993)
• Marc Roubens' example 1 (2004)
• Bernard Roy's Lausanne example (1995)
• The stability principle in question (Denis Bouyssou, October 2005)
• Roy's comment on Denis Bouyssou's argument (Bernard Roy, November 2005)
• The stability principle still in question (Marc Roubens, December 2005)

Computing digraph kernels

Hyperkernels

• Berge's suggestion for hyperkernels
• K3-C3 headed ordering
• Social Choice and the Condorcet Paradox (Taylor 2005)
• Round digraphs
• Bernard Roy's Tours example (2005)

Prekernels

• Prekernel problem of order 30
• Bernard Roy's Lausanne example (1995)
• Bernard Roy's Tours example (2005)

References

1. R. Bisdorff, P. Meyer and M. Roubens (2008). RUBIS: a bipolar-valued outranking method for the choice problem. 4OR, A Quarterly Journal of Operations Research, Springer-Verlag, Volume 6 Number 2 pp. 143-165. (Online) Electronic version: DOI: 10.1007/s10288-007-0045-5 (PDF file (227Kb) for downloading).
2. R. Bisdorff, Exploitation en problématique du choix d'une relation de surclassement valuée. Conférence invitée au séminaire "Aide à la décision" du LAMSADE. Université Paris-Dauphine, 11 octobre 2005. (PDF file (3.5Mb) for downloading).