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Fuzzy Measures and Integrals: Recent Developments

Author

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  • Michel Grabisch

    () (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

Abstract

This paper surveys the basic notions and most important results around fuzzy measures and integrals, as proposed independently by Choquet and Sugeno, as well as recent developments. The latter includes bases and transforms on set functions, fuzzy measures on set systems, the notion of horizontal additivity, basic Choquet calculus on the nonnegative real line introduced by Sugeno, the extension of the Choquet integral for nonmeasurable functions, and the notion of universal integral.

Suggested Citation

  • Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Post-Print hal-01302377, HAL.
  • Handle: RePEc:hal:journl:hal-01302377
    DOI: 10.1007/978-3-319-19683-1_8
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01302377
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    File URL: https://hal.archives-ouvertes.fr/hal-01302377/document
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    References listed on IDEAS

    as
    1. Aoi Honda & Michel Grabisch, 2008. "An axiomatization of entropy of capacities on set systems," Post-Print hal-00281598, HAL.
    2. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    3. Yaron Azrieli & Ehud Lehrer, 2007. "Extendable Cooperative Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 9(6), pages 1069-1078, December.
    4. E. Algaba & J. M. Bilbao & P. Borm & J. J. López, 2000. "The position value for union stable systems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 221-236, November.
    5. Ulrich Faigle & Michel Grabisch, 2011. "A Discrete Choquet Integral for Ordered Systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00563926, HAL.
    6. Pedro Miranda & Michel Grabisch, 2004. "p-symmetric bi-capacities," Post-Print halshs-00188173, HAL.
    7. Honda, Aoi & Grabisch, Michel, 2008. "An axiomatization of entropy of capacities on set systems," European Journal of Operational Research, Elsevier, vol. 190(2), pages 526-538, October.
    8. Ulrich Faigle & Michel Grabisch, 2014. "Linear Transforms, Values and Least Square Approximation for Cooperation Systems," Documents de travail du Centre d'Economie de la Sorbonne 14010, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    9. 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.
    10. Yaarit Even & Ehud Lehrer, 2014. "Decomposition-integral: unifying Choquet and the concave integrals," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 56(1), pages 33-58, May.
    11. repec:spr:compst:v:52:y:2000:i:2:p:221-236 is not listed on IDEAS
    12. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
    13. Grabisch, Michel, 1996. "The application of fuzzy integrals in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 89(3), pages 445-456, March.
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