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A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package

  • Michel Grabisch


    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Ivan Kojadinovic

    (LINA - Laboratoire d'Informatique de Nantes Atlantique - Mines Nantes - Mines Nantes - Institut Mines-Télécom - UN - Université de Nantes - CNRS - Centre National de la Recherche Scientifique)

  • Patrick Meyer


    (Lab-STICC_TB_CID_DECIDE - Applied Mathematic Unit - - Université du Luxembourg)

The application of multi-attribute utility theory whose aggregation process is based on the Choquet integral requires the prior identification of a capacity. The main approaches to capacity identification proposed in the literature are reviewed and their advantages and inconveniences are discussed. All the reviewed methods have been implemented within the Kappalab R package. Their application is illustrated on a detailed example.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00187175.

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Date of creation: Apr 2008
Date of revision:
Publication status: Published in European Journal of Operational Research, Elsevier, 2008, 186 (2), pp.766-785. <10.1016/j.ejor.2007.02.025>
Handle: RePEc:hal:cesptp:halshs-00187175
DOI: 10.1016/j.ejor.2007.02.025
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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;Game Theory Society, vol. 28(4), pages 547-565.
  2. Fujimoto, Katsushige & Kojadinovic, Ivan & Marichal, Jean-Luc, 2006. "Axiomatic characterizations of probabilistic and cardinal-probabilistic interaction indices," Games and Economic Behavior, Elsevier, vol. 55(1), pages 72-99, April.
  3. Marichal, Jean-Luc, 2004. "Tolerant or intolerant character of interacting criteria in aggregation by the Choquet integral," European Journal of Operational Research, Elsevier, vol. 155(3), pages 771-791, June.
  4. Marichal, Jean-Luc & Roubens, Marc, 2000. "Determination of weights of interacting criteria from a reference set," European Journal of Operational Research, Elsevier, vol. 124(3), pages 641-650, August.
  5. Kojadinovic, Ivan, 2007. "Minimum variance capacity identification," European Journal of Operational Research, Elsevier, vol. 177(1), pages 498-514, February.
  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.
  7. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
  8. 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.
  9. Karatzoglou, Alexandros & Smola, Alexandros & Hornik, Kurt & Zeileis, Achim, 2004. "kernlab - An S4 Package for Kernel Methods in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i09).
  10. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  11. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
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