Quasi-polynomial functions on bounded chains
Marichal, Jean-Luc; Couceiro, Miguel (2009), Quasi-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. 531-536
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)Two emergent properties in aggregation theory are in-vestigated, namely horizontal maxitivity and comonotonic maxitivity (as well as their dual counterparts) which are commonly deﬁned by means of certain functional equations. We present complete descrip-tions of the function classes axiomatized by each of these proper-ties, up to weak versions of monotonicity, in the cases of horizontal maxitivity and minitivity. While studying the classes axiomatized by combinations of these properties, we introduce the concept of quasi-polynomial function which appears as a natural extension of the well-established notion of polynomial function. We present further axiomatizations for this class both in terms of functional equations and natural relaxations of homogeneity and median decomposabil-ity. As noteworthy particular cases, we investigate those subclasses of quasi-term functions and quasi-weighted maximum and minimum functions, and present characterizations accordingly.
Subjects / KeywordsDiscrete Sugeno integral; quasi-polynomial function; horizontal maxitivity and minitivity; comonotonic maxitivity and minitivity; functional equation
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