Reference : Polynomial functions on bounded chains
 Document type : Scientific congresses, symposiums and conference proceedings : Paper published in a book Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics To cite this reference: http://hdl.handle.net/10993/9594
 Title : Polynomial functions on bounded chains Language : English 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 >] Publication date : 2009 Main document 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) Editor : Carvalho, J.-P. Dubois, D. Kaymak, U. Sousa, J. M. C. Pages : 525-530 Peer reviewed : Yes On invitation : No Audience : International ISBN : 978-989-95079-6-8 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 date : from 20-07-2009 to 24-07-2009 Event place (city) : Lisbon Event country : Portugal Keywords : [en] 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. Funders : University of Luxembourg - UL Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/9594 Other URL : http://www.eusflat.org/publications_proceedings_IFSA-EUSFLAT_2009.php

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