Reference : Axiomatizations of quasi-polynomial functions on bounded chains
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/2811
Axiomatizations of quasi-polynomial functions on bounded chains
English
Couceiro, Miguel mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit > ; University Paris-Dauphine > Lamsade]
Marichal, Jean-Luc mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Oct-2009
Aequationes Mathematicae
Springer
78
1-2
195-213
Yes (verified by ORBilu)
International
0001-9054
1420-8903
Basel
Switzerland
[en] aggregation function ; discrete Sugeno integral ; polynomial function ; quasi-polynomial function ; horizontal maxitivity and minitivity ; comonotonic maxitivity and minitivity ; functional equation
[en] Two emergent properties in aggregation theory are investigated, namely horizontal maxitivity and comonotonic maxitivity (as well as their dual counterparts) which are commonly defined by means of certain functional equations. We completely describe the function classes axiomatized by each of these properties, 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 give further axiomatizations for this class both in terms of functional equations and natural relaxations of homogeneity and median decomposability. As noteworthy particular cases, we investigate those subclasses of quasi-term functions and quasi-weighted maximum and minimum functions, and provide characterizations accordingly.
http://hdl.handle.net/10993/2811
10.1007/s00010-009-2969-7
http://arxiv.org/abs/0811.3913

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