lattice polynomial function; discrete Sugeno integral; term function; normal form; standard simplex; homogeneity; strong idempotency; median decomposability; comonotonicity
Abstract :
[en] We are interested in representations and characterizations of lattice polynomial functions f: L^n --> L, where L is a given bounded distributive lattice. In companion papers [5,6], we investigated certain representations and provided various characterizations of these functions both as solutions of certain functional equations and in terms of necessary and sufficient conditions. In the present paper, we investigate these representations and characterizations in the special case when L is a chain, i.e., a totally ordered lattice. More precisely, we discuss representations of lattice polynomial functions given in terms of standard simplices and we present new axiomatizations of these functions by relaxing some of the conditions given in [5,6] and by considering further conditions, namely comonotonic minitivity and maxitivity.
Disciplines :
Mathematics
Identifiers :
UNILU:UL-ARTICLE-2010-145
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 :
Representations and characterizations of polynomial functions on chains
Publication date :
2010
Journal title :
Journal of Multiple-Valued Logic and Soft Computing
ISSN :
1542-3980
Publisher :
Old City Publishing, Inc., Philadelphia, United States - Pennsylvania