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An axiomatization of entropy of capacities on set systems

Author

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  • Aoi Honda

    (Kyutech - Kyushu Institute of Technology)

  • Michel Grabisch

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

Abstract

We present an axiomatization of the entropy of capacities defined on set systems which are not necessarily the whole power set, but satisfy a condition of regularity. This entropy encompasses the definition of Marichal and Roubens for the entropy of capacities. Its axiomatization is in the spirit of the one of Faddeev for the classical Shannon entropy. In addition, we present also an axiomatization of the entropy for capacities proposed by Dukhovny

Suggested Citation

  • Aoi Honda & Michel Grabisch, 2008. "An axiomatization of entropy of capacities on set systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00281598, HAL.
    • Handle: RePEc:hal:cesptp:hal-00281598
    DOI: 10.1016/j.ejor.2007.06.033
    Note: View the original document on HAL open archive server: https://hal.science/hal-00281598
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    References listed on IDEAS

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    1. Lange, Fabien & Grabisch, Michel, 2009. "Values on regular games under Kirchhoff's laws," Mathematical Social Sciences, Elsevier, vol. 58(3), pages 322-340, November.
    2. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2018. "An axiomatisation of the Banzhaf value and interaction index for multichoice games," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02381119, HAL.
    3. Marichal, Jean-Luc, 2002. "Entropy of discrete Choquet capacities," European Journal of Operational Research, Elsevier, vol. 137(3), pages 612-624, March.
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    Cited by:

    1. Lijue Xie & Michel Grabisch, 2009. "The core of games on k-regular set systems," Post-Print halshs-00423922, HAL.
    2. Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Post-Print hal-01302377, HAL.
    3. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Annals of Operations Research, Springer, vol. 191(1), pages 137-154, November.
    4. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.

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