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A characterization of the 2-additive Choquet integral through cardinal information

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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 to represent a cardinal preferential information by the Choquet integral w.r.t. a 2-additive capacity. These conditions are based on some complex cycles called cyclones.

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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-00625708.

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Date of creation: 01 Dec 2011
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Publication status: Published, Fuzzy Sets and Systems, 2011, 184, 1, 84-105
Handle: RePEc:hal:cesptp:halshs-00625708

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00625708
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Related research

Keywords: MCDA; Choquet integral; 2-Additive capacity; MACBETH methodology;

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References

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  1. 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.
  2. 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.
  3. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
  4. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, Elsevier, vol. 17(3), pages 263-283, June.
  5. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  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. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
  8. 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.
  9. 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.
  10. 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).
  11. 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.
  12. 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.
  13. 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.
  14. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
  15. Mousset, Céline, 2009. "Families of relations modelling preferences under incomplete information," European Journal of Operational Research, Elsevier, Elsevier, vol. 192(2), pages 538-548, January.
  16. Michel Grabisch & Jacques Duchêne & Frédéric Lino & Patrice Perny, 2002. "Subjective Evaluation of Discomfort in Sitting Position," Post-Print halshs-00273179, HAL.
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Citations

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Cited by:
  1. 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.
  2. 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.

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