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An axiomatization of entropy of capacities on set systems

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  • Aoi Honda

    () (Kyushu Institute of Technology - KIT)

  • Michel Grabisch

    () (LIP6 - Laboratoire d'Informatique de Paris 6 - CNRS : UMR7606 - Université Paris VI - Pierre et Marie Curie, CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

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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Bibliographic Info

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
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Publication status: Published, European Journal of Operational Research, 2008, 190, 2, 526-538
Handle: RePEc:hal:cesptp:hal-00281598

Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00281598
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Related research

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

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  1. Fabien Lange & Michel Grabisch, 2009. "Values on regular games under Kirchhoff's laws," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00496553, HAL.
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Cited by:
  1. Michel Grabisch, 2011. "Ensuring the boundedness of the core of games with restricted cooperation," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00650964, HAL.

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