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

  • Michel Grabisch

    ()

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

  • Christophe Labreuche

    ()

    (Thales Research and Technology [Palaiseau] - THALES)

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.

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

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Date of creation: Jan 2002
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Handle: RePEc:hal:journl:halshs-00273184
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00273184
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  1. 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.
  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. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  4. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  5. 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.
  6. 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.
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