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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

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tema_0531-1.pdf (122.6Kb)
Type
Communication / Conférence
Date
2009
Conference title
13th International Fuzzy Systems Association World Congress and 6th International Conference of the European Society for Fuzzy Logic and Technology Conference (IFSA-EUSFLAT 2009)
Conference date
2009-07
Conference city
Lisbonne
Conference country
Portugal
Book title
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.
Book author
Sousa, J.M.C.; Kaymak, U.; Dubois, D.; Carvalho, J.P.
Publisher
European Society for Fuzzy Logic and Technology
ISBN
978-989-95079-6-8
Number of pages
1930
Pages
531-536
Metadata
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Author(s)
Marichal, Jean-Luc
Couceiro, Miguel
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 / Keywords
Discrete Sugeno integral; quasi-polynomial function; horizontal maxitivity and minitivity; comonotonic maxitivity and minitivity; functional equation

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