aggregation function; discrete Sugeno integral; polynomial function; quasi-polynomial function; horizontal maxitivity and minitivity; comonotonic maxitivity and minitivity; functional equation
Abstract :
[en] Two emergent properties in aggregation theory are investigated, namely horizontal maxitivity and comonotonic maxitivity (as well as their dual counterparts) which are commonly defined by means of certain functional equations. We completely describe the function classes axiomatized by each of these properties, up to weak versions of monotonicity in the cases of horizontal maxitivity and minitivity. While studying the classes axiomatized by combinations of these properties, we introduce the concept of quasi-polynomial function which appears as a natural extension of the well-established notion of polynomial function. We give further axiomatizations for this class both in terms of functional equations and natural relaxations of homogeneity and median decomposability. As noteworthy particular cases, we investigate those subclasses of quasi-term functions and quasi-weighted maximum and minimum functions, and provide characterizations accordingly.
Disciplines :
Mathematics
Identifiers :
UNILU:UL-ARTICLE-2010-144
Author, co-author :
COUCEIRO, Miguel ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit ; University Paris-Dauphine > Lamsade
MARICHAL, Jean-Luc ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Axiomatizations of quasi-polynomial functions on bounded chains
scite shows how a scientific paper has been cited by providing the context of the citation, a classification describing whether it supports, mentions, or contrasts the cited claim, and a label indicating in which section the citation was made.
Bibliography
Similar publications
Sorry the service is unavailable at the moment. Please try again later.