Reference : An axiomatic approach to the definition of the entropy of a discrete Choquet capacity
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Engineering, computing & technology : Computer science
Business & economic sciences : Quantitative methods in economics & management
http://hdl.handle.net/10993/2856
An axiomatic approach to the definition of the entropy of a discrete Choquet capacity
English
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]
9-Jun-2005
Information Sciences
Elsevier Science
172
1-2
131-153
Yes (verified by ORBilu)
International
0020-0255
[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
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/2856
10.1016/j.ins.2004.05.011

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