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A Representation of Preferences by the Choquet Integral with Respect to a 2-Additive Capacity

  • Brice Mayag

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

  • Michel Grabisch

    ()

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

  • Christophe Labreuche

    ()

    (UMP CNRS/THALES - Unité mixte de physique CNRS/Thalès - THALES - CNRS - Centre National de la Recherche Scientifique)

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00625706.

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Date of creation: 2011
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Publication status: Published in Theory and Decision, Springer Verlag, 2011, 71 (3), pp.297-324. <10.1007/s11238-010-9198-3>
Handle: RePEc:hal:cesptp:halshs-00625706
DOI: 10.1007/s11238-010-9198-3
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00625706
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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  1. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
  2. Alain Chateauneuf & Robert Kast & André Lapied, 2001. "Conditioning Capacities and Choquet Integrals: The Role of Comonotony," Theory and Decision, Springer, vol. 51(2), pages 367-386, December.
  3. WEYMARK, John A., . "Generalized Gini inequality indices," CORE Discussion Papers RP 453, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Michel Grabisch & Christophe Labreuche, 2008. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00267932, HAL.
  5. Bana e Costa, Carlos A. & Nunes da Silva, Fernando & Vansnick, Jean-Claude, 2001. "Conflict dissolution in the public sector: A case-study," European Journal of Operational Research, Elsevier, vol. 130(2), pages 388-401, April.
  6. Pedro Miranda & Michel Grabisch & Pedro Gil, 2005. "Axiomatic structure of k-additive capacities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00188165, HAL.
  7. Gajdos, Thibault, 2002. "Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities," Journal of Economic Theory, Elsevier, vol. 106(1), pages 190-200, September.
  8. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  9. 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.
  10. Cliville, Vincent & Berrah, Lamia & Mauris, Gilles, 2007. "Quantitative expression and aggregation of performance measurements based on the MACBETH multi-criteria method," International Journal of Production Economics, Elsevier, vol. 105(1), pages 171-189, January.
  11. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
  12. Jaffray, Jean-Yves & Wakker, Peter, 1993. "Decision Making with Belief Functions: Compatibility and Incompatibility with the Sure-Thing Principle," Journal of Risk and Uncertainty, Springer, vol. 7(3), pages 255-71, December.
  13. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  14. Alain Chateauneuf & Michel Grabisch & Agnès Rico, 2008. "Modeling attitudes toward uncertainty through the use of the Sugeno integral," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00327700, HAL.
  15. Marchant, Thierry, 2003. "Towards a theory of MCDM: stepping away from social choice theory," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 343-363, July.
  16. Bana e Costa, Carlos A. & Corrêa, Émerson C. & De Corte, Jean-Marie & Vansnick, Jean-Claude, 2002. "Facilitating bid evaluation in public call for tenders: a socio-technical approach," Omega, Elsevier, vol. 30(3), pages 227-242, June.
  17. Michel Grabisch & Jacques Duchêne & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Position," Post-Print halshs-00273179, HAL.
  18. 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.
  19. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
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