On the moments and the distribution of the Choquet integral

Kojadinovic, Ivan; Marichal, Jean-Luc

Reference : On the moments and the distribution of the Choquet integral


	Document type :	Scientific congresses, symposiums and conference proceedings : Paper published in a book
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics Business & economic sciences : Quantitative methods in economics & management
	To cite this reference:	http://hdl.handle.net/10993/10982

Title :	On the moments and the distribution of the Choquet integral
Language :	English
Author, co-author :	Kojadinovic, Ivan [Ecole polvtechnique de l'Université de Nantes, Nantes, France > LINA CNRS FRE 2729]
	Marichal, Jean-Luc [University of Luxembourg > Faculty of Law, Economics and Finance > Applied Mathematics Unit (SMA)]
Publication date :	Sep-2007
Main document title :	New Dimensions in Fuzzy Logic and Related Technologies. Proceedings of the 5th EUSFLAT Conference, Ostrava, Czech Republic, September 11-14, 2007. Volume I: Invited Lectures and Special Sessions
Editor :	Štěpnička, Martin
	Novák, Vilém
	Bodenhofer, Ulrich
Publisher :	Universitas Ostraviensis
Pages :	305-312
Peer reviewed :	Yes
On invitation :	No
Audience :	International
ISBN :	978-80-7368-386-3
City :	Ostrava
Country :	Czech Republic
Event name :	5th Conf. of the Eur. Society for Fuzzy Logic and Technology (EUSFLAT 2007)
Event date :	from 11-09-2007 to 14-09-2007
Event place (city) :	Ostrava
Event country :	Czech Republic
Keywords :	[en] discrete Choquet integral ; Lovász extension ; order statistic ; distribution function ; moment ; B-spline ; divided difference ; moment approximation ; asymptotic distribution
Abstract :	[en] We investigate the distribution functions and the moments of the so-called Choquet integral, also known as the Lovász extension, when regarded as a real function of a random sample drawn from a continuous population. Since the Choquet integral includes weighted arithmetic means, ordered weighted averaging operators, and lattice polynomials as particular cases, our results encompass the corresponding results for these aggregation operators. After recalling the results obtained by the authors in the uniform case, we present approaches that can be used in the non-uniform case to obtain moment approximations.
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/10993/10982
Other URL :	http://www.eusflat.org/publications_proceedings_EUSFLAT_2007.php

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Open access	MomentsChoquetIntegral.pdf		Author postprint	211.03 kB	View/Open
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Open access	EUSFLAT2007-Transparencies.pdf	Slides	138.18 kB	View/Open
Open access	Programme.pdf	Program	160.01 kB	View/Open

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