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A consolidated approach to the axiomatization of outranking relations: a survey and new results

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  • Denis Bouyssou

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  • Marc Pirlot

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Abstract

Outranking relations such as produced by the Electre I or II or the Tactic methods are based on a concordance and 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 and does not require a detailed analysis of tradeoffs between the various attributes. However, it is well known that it may produce binary relations that do not possess any remarkable property of transitivity or completeness. The axiomatic foundations of outranking relations have recently received attention. Within a conjoint measurement framework, characterizations of reflexive concordance–discordance relations have been obtained. These relations encompass those generated by the Electre I and II methods, which are non-strict (reflexive) relations. A different characterization has been provided for strict (asymmetric) preference relations such as produced by Tactic. In this paper we briefly review the various kinds of axiomatizations of outranking relations proposed so far in the literature. Then we analyze the relationships between reflexive and asymmetric outranking relations in a conjoint measurement framework, consolidating our previous work. Co-duality plays an essential rôle in our analysis. It allows us to understand the correspondence between the previous characterizations. Making a step further, we provide a common axiomatic characterization for both types of relations. Applying the co-duality operator to concordance–discordance relations also yields a new and interesting type of preference relation that we call concordance relation with bonus. The axiomatic characterization of such relations results directly from co-duality arguments. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • 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.
  • Handle: RePEc:spr:annopr:v:229:y:2015:i:1:p:159-212:10.1007/s10479-015-1803-y
    DOI: 10.1007/s10479-015-1803-y
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    References listed on IDEAS

    as
    1. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 217-245, April.
    2. Bouyssou, Denis & Pirlot, Marc, 2005. "A characterization of concordance relations," European Journal of Operational Research, Elsevier, vol. 167(2), pages 427-443, December.
    3. Bouyssou, Denis & Pirlot, Marc, 2005. "Following the traces:: An introduction to conjoint measurement without transitivity and additivity," European Journal of Operational Research, Elsevier, vol. 163(2), pages 287-337, June.
    4. Bouyssou, Denis, 1986. "Some remarks on the notion of compensation in MCDM," European Journal of Operational Research, Elsevier, vol. 26(1), pages 150-160, July.
    5. Marchant, Thierry, 2007. "An axiomatic characterization of different majority concepts," European Journal of Operational Research, Elsevier, vol. 179(1), pages 160-173, May.
    6. Deparis, Stéphane & Mousseau, Vincent & Öztürk, Meltem & Pallier, Christophe & Huron, Caroline, 2012. "When conflict induces the expression of incomplete preferences," European Journal of Operational Research, Elsevier, vol. 221(3), pages 593-602.
    7. Iverson, G. & Falmagne, J. -C., 1985. "Statistical issues in measurement," Mathematical Social Sciences, Elsevier, vol. 10(2), pages 131-153, October.
    8. repec:dau:papers:123456789/2944 is not listed on IDEAS
    9. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    10. Bouyssou, Denis & Pirlot, Marc, 2007. "Further results on concordance relations," European Journal of Operational Research, Elsevier, vol. 181(1), pages 505-514, August.
    11. Bouyssou, Denis & Pirlot, Marc, 2009. "An axiomatic analysis of concordance-discordance relations," European Journal of Operational Research, Elsevier, vol. 199(2), pages 468-477, December.
    12. Peter C. Fishburn, 1970. "Intransitive Indifference in Preference Theory: A Survey," Operations Research, INFORMS, vol. 18(2), pages 207-228, April.
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