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

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Author Info

  • Brice Mayag

    (LGI - Laboratoire Génie Industriel - EA 2606 - Ecole Centrale Paris)

  • Michel Grabisch

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Christophe Labreuche

    ()
    (UMP CNRS/THALES - Unité mixte de physique CNRS/Thalès - CNRS : UMR137 - THALES)

Abstract

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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Bibliographic Info

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, Theory and Decision, 2011, 71, 3, 297-324
Handle: RePEc:hal:cesptp:halshs-00625706

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Related research

Keywords: multicriteria decision making; Choquet integral; 2-additive capacity; MACBETH;

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  1. 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, Elsevier, vol. 130(2), pages 388-401, April.
  2. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
  3. Alain Chateauneuf & Robert Kast & André Lapied, 2001. "Conditioning Capacities and Choquet Integrals: The Role of Comonotony," Theory and Decision, Springer, Springer, vol. 51(2), pages 367-386, December.
  4. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, Springer, vol. 5(4), pages 297-323, October.
  5. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
  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. Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, Elsevier, vol. 89(3), pages 445-456, March.
  8. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  9. 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, Elsevier, vol. 105(1), pages 171-189, January.
  10. 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, Springer, vol. 7(3), pages 255-71, December.
  11. 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, Elsevier, vol. 30(3), pages 227-242, June.
  12. Gajdos, Thibault, 2002. "Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities," Journal of Economic Theory, Elsevier, Elsevier, vol. 106(1), pages 190-200, September.
  13. WEYMARK, John A., . "Generalized Gini inequality indices," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -453, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Michel Grabisch & Christophe Labreuche & Jean-Claude Vansnick, 2003. "On the Extension of Pseudo-Boolean Functions for the Aggregation of Interacting Criteria," Post-Print hal-00272780, HAL.
  15. Michel Grabisch & Christophe Labreuche, 2010. "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-00496558, HAL.
  16. 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.
  17. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
  18. Michel Grabisch & Jacques Duchêne & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Position," Post-Print halshs-00273179, HAL.
  19. Marchant, Thierry, 2003. "Towards a theory of MCDM: stepping away from social choice theory," Mathematical Social Sciences, Elsevier, Elsevier, vol. 45(3), pages 343-363, July.
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Citations

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Cited by:
  1. Silvia Bortot & Ricardo Alberto Marques Pereira, 2011. "Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process," DISA Working Papers, Department of Computer and Management Sciences, University of Trento, Italy 2011/06, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2011.
  2. Alessio Bonetti & Silvia Bortot & Mario Fedrizzi & Silvio Giove & Ricardo Alberto Marques Pereira & Andrea Molinari, 2011. "Modelling group processes and effort estimation in Project Management using the Choquet integral: an MCDM approach," DISA Working Papers, Department of Computer and Management Sciences, University of Trento, Italy 2011/12, Department of Computer and Management Sciences, University of Trento, Italy, revised Sep 2011.

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