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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. Marc Roubens & Michel Grabisch, 1999. "An axiomatic approach to the concept of interaction among players in cooperative games," International Journal of Game Theory, Springer, vol. 28(4), pages 547-565.
  2. 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.
  3. 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.
  4. 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.
  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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Citations

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Cited by:
  1. Michel Grabisch & Christophe Labreuche, 2002. "The Symmetric and Asymmetric Choquet integrals on finite spaces fordecision making," Post-Print halshs-00273184, HAL.
  2. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A characterization of the 2-additive Choquet integral through cardinal information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00625708, HAL.
  3. Michel Grabisch, 2006. "Evaluation subjective," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00179068, HAL.
  4. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
  5. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A Representation of Preferences by the Choquet Integral with Respect to a 2-Additive Capacity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00625706, HAL.
  6. 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.
  7. 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.
  8. Michel Grabisch & Ivan Kojadinovic & Patrick Meyer, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," Post-Print halshs-00187175, HAL.
  9. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
  10. Pedro Miranda & Michel Grabisch & Pedro Gil, 2005. "Axiomatic structure of k-additive capacities," Post-Print hal-00188165, HAL.
  11. 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.

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