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A note on the asymmetric part of an outranking relation

Author

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  • 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

This paper discusses the properties of the asymmetric part of an outranking relation built as in ELECTRE. Such relations have been used in the pseudodisjunctive version of ELECTRE TRI-B. We show that they have properties that are somewhat different from that of outranking relations. Indeed, contrary to outranking relations, they allow to have at the same time veto and bonus effects. We suggest that this explains the difficulty in analyzing the properties of the pseudodisjunctive version of ELECTRE TRI-B and the complexity of the elicitation methods of its parameters. We present conditions that characterize such relations.

Suggested Citation

  • Denis Bouyssou & Marc Pirlot, 2015. "A note on the asymmetric part of an outranking relation," Post-Print hal-01326876, HAL.
    • Handle: RePEc:hal:journl:hal-01326876
    DOI: 10.1111/itor.12135
    Note: View the original document on HAL open archive server: https://hal.science/hal-01326876
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    References listed on IDEAS

    as
    1. Denis Bouyssou & Marc Pirlot, 2002. "Nontransitive Decomposable Conjoint Measurement," Post-Print hal-02361942, HAL.
    2. Dias, Luis C. & Mousseau, Vincent, 2006. "Inferring Electre's veto-related parameters from outranking examples," European Journal of Operational Research, Elsevier, vol. 170(1), pages 172-191, April.
    3. Dias, Luis & Mousseau, Vincent & Figueira, Jose & Climaco, Joao, 2002. "An aggregation/disaggregation approach to obtain robust conclusions with ELECTRE TRI," European Journal of Operational Research, Elsevier, vol. 138(2), pages 332-348, April.
    4. Cailloux, Olivier & Meyer, Patrick & Mousseau, Vincent, 2012. "Eliciting Electre Tri category limits for a group of decision makers," European Journal of Operational Research, Elsevier, vol. 223(1), pages 133-140.
    5. Luis Dias & João Clímaco, 2000. "ELECTRE TRI for Groups with Imprecise Information on Parameter Values," Group Decision and Negotiation, Springer, vol. 9(5), pages 355-377, September.
    6. Denis Bouyssou & Thierry Marchant, 2013. "Some remarks on ELECTRE TRI," Working Papers hal-00942310, HAL.
    7. Mousseau, V. & Figueira, J. & Naux, J. -Ph., 2001. "Using assignment examples to infer weights for ELECTRE TRI method: Some experimental results," European Journal of Operational Research, Elsevier, vol. 130(2), pages 263-275, April.
    8. Almeida-Dias, J. & Figueira, J.R. & Roy, B., 2010. "Electre Tri-C: A multiple criteria sorting method based on characteristic reference actions," European Journal of Operational Research, Elsevier, vol. 204(3), pages 565-580, August.
    9. Denis Bouyssou & Marc Pirlot, 2004. "Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations," Post-Print hal-00004104, HAL.
    10. Mousseau, Vincent & Figueira, Jose & Dias, Luis & Gomes da Silva, Carlos & Climaco, Joao, 2003. "Resolving inconsistencies among constraints on the parameters of an MCDA model," European Journal of Operational Research, Elsevier, vol. 147(1), pages 72-93, May.
    11. repec:dau:papers:123456789/1482 is not listed on IDEAS
    12. Mousseau, Vincent & Dias, Luis, 2004. "Valued outranking relations in ELECTRE providing manageable disaggregation procedures," European Journal of Operational Research, Elsevier, vol. 156(2), pages 467-482, July.
    13. Bouyssou, Denis & Pirlot, Marc, 2007. "Further results on concordance relations," European Journal of Operational Research, Elsevier, vol. 181(1), pages 505-514, August.
    14. Bertrand Mareschal & Jean Pierre Brans & Philippe Vincke, 1986. "How to select and how to rank projects: the Prométhée method," ULB Institutional Repository 2013/9307, ULB -- Universite Libre de Bruxelles.
    15. Brans, J. P. & Vincke, Ph. & Mareschal, B., 1986. "How to select and how to rank projects: The method," European Journal of Operational Research, Elsevier, vol. 24(2), pages 228-238, February.
    16. Sébastien Damart & Luis Dias & Vincent Mousseau, 2007. "Supporting groups in sorting decisions: methodology and use of a multi-criteria aggregation-disaggregation DSS," Post-Print halshs-00170234, HAL.
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    Cited by:

    1. Eduardo Fernández & José Rui Figueira & Jorge Navarro, 2023. "A theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes," Annals of Operations Research, Springer, vol. 325(2), pages 819-843, June.
    2. Eduardo Fernandez & Jose Rui Figueira & Jorge Navarro, 2021. "a theoretical look at ordinal classification methods based on comparing actions with limiting boundaries between adjacent classes," Papers 2107.03440, arXiv.org.

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