Reference : An axiomatic approach to the definition of the entropy of a discrete Choquet capacity
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Physical, chemical, mathematical & earth Sciences : Mathematics
Engineering, computing & technology : Computer science
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An axiomatic approach to the definition of the entropy of a discrete Choquet capacity
Kojadinovic, Ivan mailto [École polytechnique de l’Université de Nantes, Nantes, France > LINA CNRS FRE 2729]
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Applied Mathematics Unit (SMA)]
Roubens, Marc [University of Liège, Belgium > Institute of Mathematics]
Information Sciences
Elsevier Science
Yes (verified by ORBilu)
[en] entropy ; choquet capacity ; choquet integral ; information theory
[en] To extend the classical Shannon entropy to non-additive measures, Marichal recently introduced the concept of generalized entropy for discrete Choquet capacities. We provide a first axiomatization of this new concept on the basis of three axioms: the symmetry property, a boundary condition for which the entropy reduces to the Shannon entropy, and a generalized version of the well-known recursivity property. We also show that this generalized entropy fulfills several properties considered as requisites for defining an entropy-like measure. Lastly, we provide an interpretation of it in the framework of aggregation by the discrete Choquet integral.
University of Luxembourg - UL
Recherches méthodologiques et mathématiques en aide à la décision et à la classification > 01/01/2005 – 12/12/2007 > BISDORFF Raymond
Researchers ; Professionals ; Students

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