Reference : An axiomatic approach to the definition of the entropy of a discrete Choquet capacity

	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics Engineering, computing & technology : Computer science Business & economic sciences : Quantitative methods in economics & management
	To cite this reference:	http://hdl.handle.net/10993/2856

Title :	An axiomatic approach to the definition of the entropy of a discrete Choquet capacity
Language :	English
Author, co-author :	Kojadinovic, Ivan [École polytechnique de l’Université de Nantes, Nantes, France > LINA CNRS FRE 2729]
	Marichal, Jean-Luc [University of Luxembourg > Faculty of Law, Economics and Finance (FDEF) > Applied Mathematics Unit (SMA)]
	Roubens, Marc [University of Liège, Belgium > Institute of Mathematics]
Publication date :	9-Jun-2005
Journal title :	Information Sciences
Publisher :	Elsevier Science
Volume :	172
Issue/season :	1-2
Pages :	131-153
Peer reviewed :	Yes (verified by ORBilu)
Audience :	International
ISSN :	0020-0255
Keywords :	[en] entropy ; choquet capacity ; choquet integral ; information theory
Abstract :	[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.
Funders :	University of Luxembourg - UL
Name of the research project :	Recherches méthodologiques et mathématiques en aide à la décision et à la classification > 01/01/2005 – 12/12/2007 > BISDORFF Raymond
Target :	Researchers ; Professionals ; Students
Permalink :	http://hdl.handle.net/10993/2856
DOI :	10.1016/j.ins.2004.05.011

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