Paper published in a book (Scientific congresses, symposiums and conference proceedings)
Quasi-polynomial functions on bounded chains
Couceiro, Miguel; Marichal, Jean-Luc
2009 • In Carvalho, J. P.; Dubois, D.; Kaymak, U.et al. (Eds.) Proc. of 2009 Int. Fuzzy Systems Assoc. World Congress and 2009 Int. Conf. of the Eur. Soc. for Fuzzy Logic and Technology (IFSA-EUSFLAT 2009 Joint Conference)
Discrete Sugeno integral; 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 quasipolynomial 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. As noteworthy particular cases, we investigate those subclasses of quasi-term functions and quasi-weighted maximum and minimum functions, and present characterizations accordingly.
Disciplines :
Mathematics
Identifiers :
UNILU:UL-CONFERENCE-2010-196
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 :
Quasi-polynomial functions on bounded chains
Publication date :
2009
Event name :
2009 Int. Fuzzy Systems Assoc. World Congress and 2009 Int. Conf. of the Eur. Soc. for Fuzzy Logic and Technology (IFSA-EUSFLAT 2009 Joint Conference)
Event place :
Lisbon, Portugal
Event date :
from 20-07-2009 to 24-07-2009
Audience :
International
Main work title :
Proc. of 2009 Int. Fuzzy Systems Assoc. World Congress and 2009 Int. Conf. of the Eur. Soc. for Fuzzy Logic and Technology (IFSA-EUSFLAT 2009 Joint Conference)