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

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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)

  • Jean-Claude Vansnick

    (University of Mons-Hainaut - University of Mons-Hainaut)

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.

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Bibliographic Info

Paper provided by HAL in its series Post-Print with number hal-00272780.

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Date of creation: 2003
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Publication status: Published, European Journal of Operational Research, 2003, 28-47
Handle: RePEc:hal:journl:hal-00272780

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00272780/en/
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References

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  1. Grabisch, M. & Roubens, M., 1998. "An Axiomatic Approach to the Concept of Interaction Among Players in Cooperative Games," Liege - Groupe d'Etude des Mathematiques du Management et de l'Economie 9818, UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie.
  2. 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.
  3. 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.
  4. 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.
  5. 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.
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Cited by:
  1. repec:hal:journl:halshs-00187175 is not listed on IDEAS
  2. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
  3. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
  4. Michel Grabisch & Christophe Labreuche, 2002. "The symmetric and asymmetric Choquet integrals on finite spaces for decision making," Statistical Papers, Springer, vol. 43(1), pages 37-52, January.
  5. repec:hal:journl:hal-00188165 is not listed on IDEAS
  6. Caterina Cruciani & Silvio Giove & Mehmet Pinar & Matteo Sostero, 2013. "Constructing the FEEM Sustainability Index: A Choquet-integral Application," Working Papers 2013.16, Fondazione Eni Enrico Mattei.
  7. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
  8. repec:hal:cesptp:halshs-00625708 is not listed on IDEAS
  9. repec:hal:cesptp:halshs-00179068 is not listed on IDEAS
  10. Silvia Bortot & Mario Fedrizzi & Silvio Giove, 2011. "Modelling fraud detection by attack trees and Choquet integral," DISA Working Papers 2011/09, Department of Computer and Management Sciences, University of Trento, Italy, revised 31 Aug 2011.
  11. Borgonovo, E. & Smith, C.L., 2012. "Composite multilinearity, epistemic uncertainty and risk achievement worth," European Journal of Operational Research, Elsevier, vol. 222(2), pages 301-311.

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