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


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)


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

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  1. 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.
  2. 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, UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et 9818, UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie.
  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. 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, Elsevier, vol. 17(3), pages 263-283, June.
  5. 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, Elsevier, vol. 113(2), pages 315-335, March.
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Cited by:
  1. Borgonovo, E. & Smith, C.L., 2012. "Composite multilinearity, epistemic uncertainty and risk achievement worth," European Journal of Operational Research, Elsevier, Elsevier, vol. 222(2), pages 301-311.
  2. Silvia Bortot & Mario Fedrizzi & Silvio Giove, 2011. "Modelling fraud detection by attack trees and Choquet integral," DISA Working Papers, Department of Computer and Management Sciences, University of Trento, Italy 2011/09, Department of Computer and Management Sciences, University of Trento, Italy, revised 31 Aug 2011.
  3. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
  4. repec:hal:journl:hal-00188165 is not listed on IDEAS
  5. 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, Springer, vol. 71(3), pages 297-324, September.
  6. 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.
  7. Michel Grabisch & Christophe Labreuche, 2002. "The Symmetric and Asymmetric Choquet integrals on finite spaces fordecision making," Post-Print halshs-00273184, HAL.
  8. 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.
  9. Michel Grabisch, 2006. "Evaluation subjective," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00179068, HAL.
  10. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
  11. repec:hal:journl:halshs-00187175 is not listed on IDEAS


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