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On the moments and the distribution of the Choquet integral
Kojadinovic, Ivan; Marichal, Jean-Luc
2007In Štěpnička, Martin; Novák, Vilém; Bodenhofer, Ulrich (Eds.) 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
Peer reviewed
 

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Keywords :
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.
Disciplines :
Mathematics
Quantitative methods in economics & management
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)
Language :
English
Title :
On the moments and the distribution of the Choquet integral
Publication date :
September 2007
Event name :
5th Conf. of the Eur. Society for Fuzzy Logic and Technology (EUSFLAT 2007)
Event place :
Ostrava, Czechia
Event date :
from 11-09-2007 to 14-09-2007
Audience :
International
Main work 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, Ostrava, Czechia
ISBN/EAN :
978-80-7368-386-3
Pages :
305-312
Peer reviewed :
Peer reviewed
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
Funders :
University of Luxembourg - UL
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