Polynomial functions on bounded chains
Marichal, Jean-Luc; Couceiro, Miguel (2009), Polynomial functions on bounded chains, in Sousa, J.M.C.; Kaymak, U.; Dubois, D.; Carvalho, J.P, Proceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009., European Society for Fuzzy Logic and Technology, p. 525-530
TypeCommunication / Conférence
Conference title13th International Fuzzy Systems Association World Congress and 6th International Conference of the European Society for Fuzzy Logic and Technology Conference (IFSA-EUSFLAT 2009)
Book titleProceedings of the Joint 2009 International Fuzzy Systems Association World Congress and 2009 European Society of Fuzzy Logic and Technology Conference, Lisbon, Portugal, July 20-24, 2009.
Book authorSousa, J.M.C.; Kaymak, U.; Dubois, D.; Carvalho, J.P
Number of pages1930
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Abstract (EN)We are interested in representations and characteriza- tions of lattice polynomial functions f : Ln → L, where L is a given bounded distributive lattice. In an earlier paper [4, 5], we investi- gated 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 axiomati- zations of these functions by relaxing some of the conditions given in [4, 5] and by considering further conditions, namely comonotonic minitivity and maxitivity.
Subjects / Keywordscomonotonicity; median decomposability; strong idempotency; homogeneity; normal form; discrete Sugeno integral; Lattice polynomial function
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