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Entropy of Fuzzy Measure

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Integrated Uncertainty Management and Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 68))

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Abstract

A definition for the entropy of fuzzy measures defined on set systems is proposed. The underlying set is not necessarily the whole power set, but satisfy a condition of regularity. This definition encompasses the classical definition of Shannon for probability measures, as well as the definition of Marichal et al. for classical fuzzy measures, and may have applicability to most fuzzy measures which appear in applications. We give several characterizations of this entropy which are natural and understandable as the entropy.

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Author information

Authors and Affiliations

  1. Kyushu Institute of Technology, 680-4 Kawazu, Iizuka city, Fukuoka, 820-8502, Japan

    Aoi Honda

  2. Centre d’Économie de la Sorbonne, University of Paris I, 106-112, Bd de l’Hôpital, 75013, Paris, France

    Michel Grabisch

Authors
  1. Aoi Honda
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  2. Michel Grabisch
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Editor information

Editors and Affiliations

  1. School of Knowledge Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, 923-1292, Ishikawa, Japan

    Van-Nam Huynh  & Yoshiteru Nakamori  & 

  2. Department of Engineering Mathematics, University of Bristol, Queen’s Building, University Walk, BS8 1TR, Bristol, United Kingdom

    Jonathan Lawry

  3. Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, 560-8531, Osaka, Japan

    Masahiro Inuiguchi

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Honda, A., Grabisch, M. (2010). Entropy of Fuzzy Measure. In: Huynh, VN., Nakamori, Y., Lawry, J., Inuiguchi, M. (eds) Integrated Uncertainty Management and Applications. Advances in Intelligent and Soft Computing, vol 68. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11960-6_11

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  • DOI: https://doi.org/10.1007/978-3-642-11960-6_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-11959-0

  • Online ISBN: 978-3-642-11960-6

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