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The Symmetric and Asymmetric Choquet integrals on finite spaces for decision making

Author

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  • Michel Grabisch

    () (SYSDEF - Systèmes d'aide à la décision et à la formation - LIP6 - Laboratoire d'Informatique de Paris 6 - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique)

  • Christophe Labreuche

    () (Thales Research and Technology [Palaiseau] - THALES)

Abstract

In this paper, we give a mathematical analysis of symmetric and asymmetric Choquet integrals in the view of decision making in a finite setting. These integrals present two ways of dealing with negative integrands. The analysis is done with the aid of the Möbius and interaction transforms, this last one having an interesting interpretation in multicriteria decision making (MCDM). The last part of the paper shows the application of these two integrals in MCDM.

Suggested Citation

  • Michel Grabisch & Christophe Labreuche, 2002. "The Symmetric and Asymmetric Choquet integrals on finite spaces for decision making," Post-Print halshs-00273184, HAL.
  • Handle: RePEc:hal:journl:halshs-00273184
    DOI: 10.1007/s00362-001-0085-4
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00273184
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    References listed on IDEAS

    as
    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. 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.
    3. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    4. Fabien Lange & Michel Grabisch, 2006. "Interaction transform for bi-set functions over a finite set," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00186891, HAL.
    5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Michel Grabisch, 2015. "Bases and transforms of set functions," Documents de travail du Centre d'Economie de la Sorbonne 15048, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    2. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
    3. Labreuche, Christophe & Grabisch, Michel, 2006. "Generalized Choquet-like aggregation functions for handling bipolar scales," European Journal of Operational Research, Elsevier, vol. 172(3), pages 931-955, August.
    4. repec:hal:journl:halshs-01169287 is not listed on IDEAS
    5. Kojadinovic, Ivan & Marichal, Jean-Luc, 2007. "Entropy of bi-capacities," European Journal of Operational Research, Elsevier, vol. 178(1), pages 168-184, April.
    6. Michel Grabisch, 2003. "The Symmetric Sugeno Integral," Post-Print hal-00272084, HAL.
    7. Kojadinovic, Ivan, 2007. "A weight-based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar Choquet integral," European Journal of Operational Research, Elsevier, vol. 179(2), pages 498-517, June.

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