Reference : Representations and characterizations of polynomial functions on chains
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/1211
Representations and characterizations of polynomial functions on chains
English
Couceiro, Miguel mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2010
Journal of Multiple-Valued Logic & Soft Computing
Old City Publishing, Inc.
16
1-2
65-86
Yes (verified by ORBilu)
International
1542-3980
Philadelphia
PA
[en] lattice polynomial function ; discrete Sugeno integral ; term function ; normal form ; standard simplex ; homogeneity ; strong idempotency ; median decomposability ; comonotonicity
[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.
Mathematics Research Unit (FSTC)
University of Luxembourg - UL
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/1211

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