Axiomatizations of quasi-polynomial functions on bounded chains
Marichal, Jean-Luc; Couceiro, Miguel (2009), Axiomatizations of quasi-polynomial functions on bounded chains, Aequationes Mathematicae, 78, 1-2, p. 195-213. http://dx.doi.org/10.1007/s00010-009-2969-7
Type
Article accepté pour publication ou publiéExternal document link
http://arxiv.org/abs/0811.3913Date
2009Journal name
Aequationes MathematicaeVolume
78Number
1-2Publisher
Springer
Pages
195-213
Publication identifier
Metadata
Show full item recordAbstract (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 the subclasses of quasi-term functions and quasi-weighted maximum and minimum functions, and provide characterizations accordingly.Subjects / Keywords
comonotonicity; median decomposability; strong idempotency; homogeneity; standard simplex; normal form; term function; discrete Sugeno integral; Lattice polynomial functionRelated items
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