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The Symmetric and Asymmetric Choquet integrals on finite spaces fordecision making

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Author Info

  • 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)

Abstract

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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Bibliographic Info

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

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Date of creation: 2002
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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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Related research

Keywords: Choquet integral; symmetric integral; Möbius transform; interaction;

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References

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  1. Michel Grabisch & Christophe Labreuche & Jean-Claude Vansnick, 2003. "On the Extension of Pseudo-Boolean Functions for the Aggregation of Interacting Criteria," Post-Print, HAL hal-00272780, HAL.
  2. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  3. 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.
  4. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, Econometric Society, vol. 47(2), pages 263-91, March.
  5. 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.
  6. 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.
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Citations

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Cited by:
  1. Michel Grabisch, 2003. "The Symmetric Sugeno Integral," Post-Print, HAL hal-00272084, HAL.
  2. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print, HAL halshs-00268985, HAL.
  3. Kojadinovic, Ivan & Marichal, Jean-Luc, 2007. "Entropy of bi-capacities," European Journal of Operational Research, Elsevier, Elsevier, vol. 178(1), pages 168-184, April.

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