Paper published in a book (Scientific congresses, symposiums and conference proceedings)
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)
Lattice polynomial function; discrete Sugeno integral; normal form; homogeneity; strong idempotency; median decomposability; comonotonicity
Abstract :
[en] We are interested in representations and characterizations of lattice polynomial functions $f\colon L^n\to L$, where $L$ is a given bounded distributive lattice. In an earlier paper [4,5], 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 [4,5] and by considering further conditions, namely comonotonic minitivity and maxitivity.
Disciplines :
Mathematics
Identifiers :
UNILU:UL-CONFERENCE-2010-195
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 :
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)
