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An axiomatic analysis of concordance–discordance relations

Author

Listed:
  • Denis Bouyssou

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris Sciences et Lettres - CNRS - Centre National de la Recherche Scientifique)

  • Marc Pirlot

    (Faculté polytechnique de Mons - UMONS - Université de Mons = University of Mons)

Abstract

Outranking methods propose an original way to build a preference relation between alternatives evaluated on several attributes that has a definite ordinal flavor. Indeed, most of them appeal the concordance/non-discordance principle that leads to declaring that an alternative is "superior" to another, if the coalition of attributes supporting this proposition is "sufficiently important" (concordance condition) and if there is no attribute that "strongly rejects" it (non-discordance condition). Such a way of comparing alternatives is rather natural. However, it is well known that it may produce binary relations that do not possess any remarkable property of transitivity or completeness. This explains why the axiomatic foundations of outranking methods have not been much investigated, which is often seen as one of their important weaknesses. This paper uses conjoint measurement techniques to obtain an axiomatic characterization of preference relations that can be obtained on the basis of the concordance/non-discordance principle. It emphasizes their main distinctive feature, i.e. their very crude way to distinguish various levels of preference differences on each attribute. We focus on outranking methods, such as ELECTRE I, that produce a reflexive relation, interpreted as an "at least as good as" preference relation. The results in this paper may be seen as an attempt to give such outranking methods a sound axiomatic foundation based on conjoint measurement.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Denis Bouyssou & Marc Pirlot, 2009. "An axiomatic analysis of concordance–discordance relations," Post-Print hal-02361903, HAL.
    • Handle: RePEc:hal:journl:hal-02361903
    DOI: 10.1016/j.ejor.2008.11.011
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    Cited by:

    1. Denis Bouyssou & Marc Pirlot, 2015. "A consolidated approach to the axiomatization of outranking relations: a survey and new results," Annals of Operations Research, Springer, vol. 229(1), pages 159-212, June.
    2. Arayeh Afsordegan & Luis Del Vasto-Terrientes & Aida Valls & Núria Agell & Mónica Sánchez, 2022. "Finding the most sustainable wind farm sites with a hierarchical outranking decision aiding method," Annals of Operations Research, Springer, vol. 312(2), pages 1307-1335, May.
    3. Govindan, Kannan & Jepsen, Martin Brandt, 2016. "ELECTRE: A comprehensive literature review on methodologies and applications," European Journal of Operational Research, Elsevier, vol. 250(1), pages 1-29.
    4. Arwa Khannoussi & Alexandru-Liviu Olteanu & Christophe Labreuche & Patrick Meyer, 2022. "Simple ranking method using reference profiles: incremental elicitation of the preference parameters," 4OR, Springer, vol. 20(3), pages 499-530, September.
    5. Xingli Wu & Huchang Liao, 2022. "A gained and lost dominance score method with conflict analysis for green economy development evaluation," Annals of Operations Research, Springer, vol. 316(1), pages 623-655, September.
    6. Arwa Khannoussi & Alexandru-Liviu Olteanu & Patrick Meyer & Nawal Benabbou, 2024. "A regret-based query selection strategy for the incremental elicitation of the criteria weights in an SRMP model," Operational Research, Springer, vol. 24(2), pages 1-21, June.
    7. Joseph, Rémy-Robert, 2010. "Making choices with a binary relation: Relative choice axioms and transitive closures," European Journal of Operational Research, Elsevier, vol. 207(2), pages 865-877, December.

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