signed discrete Choquet integral; signed capacity; Lovász extension; functional equation; comonotonic additivity; homogeneity; axiomatization
Abstract :
[en] We study the so-called signed discrete Choquet integral (also called non-monotonic discrete Choquet integral) regarded as the Lovász extension of a pseudo-Boolean function which vanishes at the origin. We present axiomatizations of this generalized Choquet integral, given in terms of certain functional equations, as well as by necessary and sufficient conditions which reveal desirable properties in aggregation theory.
Disciplines :
Quantitative methods in economics & management Mathematics
Identifiers :
UNILU:UL-ARTICLE-2011-148
Author, co-author :
Cardin, Marta; University Ca’ Foscari of Venice, Italy > Department of Applied Mathematics
Couceiro, Miguel ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Giove, Silvio; University Ca’ Foscari of Venice, Italy > Department of Applied Mathematics
Marichal, Jean-Luc ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Axiomatizations of signed discrete Choquet integrals
Publication date :
April 2011
Journal title :
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
