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An axiomatization of entropy of capacities on set systems

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Listed author(s):
  • Aoi Honda

    ()

    (Kyushu Institute of Technology - KIT)

  • Michel Grabisch

    ()

    (CES - Centre d'économie de la Sorbonne - UP1 - Université 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

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File URL: https://hal.archives-ouvertes.fr/hal-00281598/document
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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00281598.

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Date of creation: Oct 2008
Publication status: Published in European Journal of Operational Research, Elsevier, 2008, 190 (2), pp.526-538. <10.1016/j.ejor.2007.06.033>
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.archives-ouvertes.fr/hal-00281598
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

Keywords: Entropy; Capacity; Regular set system; Generalized Faddeev's axiom;

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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. 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. 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.

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