Paper published in a book (Scientific congresses, symposiums and conference proceedings)
Axiomatizations of the discrete Choquet integral and extensions
Couceiro, Miguel; Marichal, Jean-Luc
2011 • In Galichet, Sylvie; Montero, Javier; Mauris, Gilles (Eds.) Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) and LFA-2011
[en] Three important properties in aggregation theory are investigated, namely horizontal min-additivity, horizontal max-additivity, and comonotonic additivity, which are defined by certain relaxations of the Cauchy functional equation in several variables. We show that these properties are equivalent and we completely describe the functions characterized by them. By adding some regularity conditions, the latter functions coincide with the Lovász extensions vanishing at the origin, which subsume the discrete Choquet integrals. We also propose a simultaneous generalization of horizontal min-additivity and horizontal max-additivity, called horizontal median-additivity, and we describe the corresponding function class. Additional conditions then reduce this class to that of symmetric Lovász extensions, which includes the discrete symmetric Choquet integrals.
Disciplines :
Mathematics Quantitative methods in economics & management
Identifiers :
UNILU:UL-CONFERENCE-2011-278
Author, co-author :
Couceiro, Miguel ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Marichal, Jean-Luc ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Axiomatizations of the discrete Choquet integral and extensions
Publication date :
2011
Event name :
Joint 7th Conference of the European Society for Fuzzy Logic and Technology and the 17th Rencontres Francophones sur la Logique Floue et ses Applications (2011 EUSFLAT-LFA Joint Conference)
Event place :
Aix-les-Bains, France
Event date :
from 18-07-2011 to 22-07-2011
Audience :
International
Main work title :
Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-2011) and LFA-2011