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The Symmetric and Asymmetric Choquet integrals on finite spaces fordecision making

  • Michel Grabisch

    ()

    (LIP6 - Laboratoire d'Informatique de Paris 6 - CNRS : UMR7606 - Université Pierre et Marie Curie - Paris VI)

  • Christophe Labreuche

    ()

    (TRT - Thales Research & Technology France - THALES)

In this paper, we give a mathematical analysis of symmetric and asymmetricChoquet integrals in the view of decision making in a finite setting. Theseintegrals present two ways of dealing with negative integrands. The analysis isdone with the aid of the Möbius and interaction transforms, this last onehaving an interesting interpretation in multicriteria decision making(MCDM). The last part of the paper shows the application of these two integralsin MCDM.

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Paper provided by HAL in its series Post-Print with number halshs-00273184.

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Date of creation: 2002
Date of revision:
Publication status: Published, Statistical Papers, 2002, 37-52
Handle: RePEc:hal:journl:halshs-00273184
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00273184/en/
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  1. 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.
  2. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  3. Michel Grabisch & Fabien Lange, 2006. "Interaction transform for bi-set functions over a finite set," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00186891, HAL.
  4. 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.
  5. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  6. 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.
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