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Capacities and Games on Lattices: A Survey of Result

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  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We provide a survey of recent developments about capacities (or fuzzy measures) and ccoperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.

Suggested Citation

  • Michel Grabisch, 2006. "Capacities and Games on Lattices: A Survey of Result," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00179830, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00179830
    DOI: 10.1142/S0218488506004084
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00179830
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    1. 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.
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    7. Marichal, Jean-Luc, 2002. "Entropy of discrete Choquet capacities," European Journal of Operational Research, Elsevier, vol. 137(3), pages 612-624, March.
    8. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
    9. Tijs, S.H. & Brânzei, R. & Ishihara, S. & Muto, S., 2004. "On cores and stable sets for fuzzy games," Other publications TiSEM 66dd20be-cb4b-4b6d-937e-0, Tilburg University, School of Economics and Management.
    10. Bilbao, J. M., 1998. "Axioms for the Shapley value on convex geometries," European Journal of Operational Research, Elsevier, vol. 110(2), pages 368-376, October.
    11. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-266.
    12. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
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