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On the Extension of Pseudo-Boolean Functions for the Aggregation of Interacting Criteria

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 [France])

  • Jean-Claude Vansnick

    (UMONS - University of Mons [Belgium])

Abstract

The paper presents an analysis on the use of integrals defined for non-additive measures (or capacities) as the Choquet and the \Sipos{} integral, and the multilinear model, all seen as extensions of pseudo-Boolean functions, and used as a means to model interaction between criteria in a multicriteria decision making problem. The emphasis is put on the use, besides classical comparative information, of information about difference of attractiveness between acts, and on the existence, for each point of view, of a ``neutral level'', allowing to introduce the absolute notion of attractive or repulsive act. It is shown that in this case, the Sipos integral is a suitable solution, although not unique. Properties of the Sipos integral as a new way of aggregating criteria are shown, with emphasis on the interaction among criteria.

Suggested Citation

  • 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.
    • Handle: RePEc:hal:journl:hal-00272780
    Note: View the original document on HAL open archive server: https://hal.science/hal-00272780
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    References listed on IDEAS

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    1. 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.
    2. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 547-565.
    3. 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, vol. 17(3), pages 263-283, June.
    4. Bana e Costa, Carlos A. & Ensslin, Leonardo & Correa, Emerson C. & Vansnick, Jean-Claude, 1999. "Decision Support Systems in action: Integrated application in a multicriteria decision aid process," European Journal of Operational Research, Elsevier, vol. 113(2), pages 315-335, March.
    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.
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