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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

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  • Grabisch, Michel
  • Kojadinovic, Ivan
  • Meyer, Patrick

Abstract

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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  • Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    • Handle: RePEc:eee:ejores:v:186:y:2008:i:2:p:766-785
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    1. 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.
    2. 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.
    3. 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.
    4. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    5. 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.
    6. 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.
    7. Kojadinovic, Ivan, 2007. "Minimum variance capacity identification," European Journal of Operational Research, Elsevier, vol. 177(1), pages 498-514, February.
    8. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
    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. 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.
    11. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
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