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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 - Uni.lu - 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
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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
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00187175
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  1. 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.
  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. 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.
  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, vol. 17(3), pages 263-283, June.
  5. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
  6. 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.
  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. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  9. 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.
  10. 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).
  11. Kojadinovic, Ivan, 2007. "Minimum variance capacity identification," European Journal of Operational Research, Elsevier, vol. 177(1), pages 498-514, February.
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