Paper published in a book (Scientific congresses, symposiums and conference proceedings)
From discrete Sugeno integrals to generalized lattice polynomial functions: axiomatizations and representations (invited lecture)
Couceiro, Miguel; Marichal, Jean-Luc
2009 • In González, Manuel; Mayor, Gaspar; Suner, Jaumeet al. (Eds.) Proc. 5th Int. Summer School on Aggregation Operators and their Applications (AGOP 2009)
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 present complete descriptions of 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 present further axiomatizations for this class both in terms of functional equations and natural relaxations of homogeneity and median decomposability.
Disciplines :
Mathematics
Identifiers :
UNILU:UL-CONFERENCE-2010-194
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 :
From discrete Sugeno integrals to generalized lattice polynomial functions: axiomatizations and representations (invited lecture)
Publication date :
2009
Event name :
5th Int. Summer School on Aggregation Operators and their Applications (AGOP 2009)
Event organizer :
Gaspar Mayor
Event place :
Palma de Mallorca, Spain
Event date :
from 06-07-2009 to 10-07-2009
By request :
Yes
Audience :
International
Main work title :
Proc. 5th Int. Summer School on Aggregation Operators and their Applications (AGOP 2009)
Editor :
González, Manuel
Mayor, Gaspar
Suner, Jaume
Torrens, Joan
Publisher :
Edicions UIB. Cas Jai. Campus Universitari, Universitat de Illes Balears, Spain