[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, these functions coincide with the Lovász extensions vanishing at the origin, which subsume the discrete Choquet integrals.
Disciplines :
Mathematics Quantitative methods in economics & management
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 :
On three properties of the discrete Choquet integral
Publication date :
2011
Event name :
32nd Linz Seminar on Fuzzy Set Theory (LINZ 2011)
Event organizer :
Erich Peter Klement (Chairman), Johannes Kepler University Linz
Event place :
Linz, Austria
Event date :
from 01-02-2011 to 05-02-2011
Audience :
International
Main work title :
32nd Linz Seminar on Fuzzy Set Theory (LINZ 2011) - Decision Theory: Qualitative and Quantitative Approaches
