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Representation of preferences over a finite scale by a mean operator

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  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Suppose that a decision maker provides a weak order on a given set of alternatives, each alternative being described by a vector of scores, which are given on a finite ordinal scale $E$. The paper addresses the question of the representation of this weak order by some mean operator, and gives necessary and sufficient conditions for such a representation, with possible shrinking and/or refinement of the scale $E$.

Suggested Citation

  • Michel Grabisch, 2006. "Representation of preferences over a finite scale by a mean operator," Post-Print halshs-00179069, HAL.
    • Handle: RePEc:hal:journl:halshs-00179069
    DOI: 10.1016/j.mathsocsci.2006.05.001
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00179069
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    References listed on IDEAS

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    1. Grabisch, Michel & Labreuche, Christophe & Vansnick, Jean-Claude, 2003. "On the extension of pseudo-Boolean functions for the aggregation of interacting criteria," European Journal of Operational Research, Elsevier, vol. 148(1), pages 28-47, July.
    2. Ovchinnikov, Sergei, 1996. "Means on ordered sets," Mathematical Social Sciences, Elsevier, vol. 32(1), pages 39-56, August.
    3. Dubois, Didier & Prade, Henri & Sabbadin, Regis, 2001. "Decision-theoretic foundations of qualitative possibility theory," European Journal of Operational Research, Elsevier, vol. 128(3), pages 459-478, February.
    4. Agnès Rico & Michel Grabisch & Christophe Labreuche & Alain Chateauneuf, 2005. "Preference modelling on totally ordered sets by the Sugeno integral," Post-Print hal-00268984, HAL.
    5. Denis Bouyssou & Marc Pirlot, 2004. "Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations," Post-Print hal-00004104, HAL.
    6. Denis Bouyssou & Marc Pirlot, 2004. "Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations," Post-Print hal-00004104, HAL.
    7. Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
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    Cited by:

    1. José Luis Garcí a-Lapresta & Bonifacio Llamazares, 2010. "Preference Intensities and Majority Decisions Based on Difference of Support Between Alternatives," Group Decision and Negotiation, Springer, vol. 19(6), pages 527-542, November.
    2. Marcello Basili & Stefano Vannucci, 2013. "Diversity as width," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 913-936, March.

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