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
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/0811.3913
Journal nameAequationes Mathematicae
MetadataShow full item record
Abstract (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 / Keywordscomonotonicity; median decomposability; strong idempotency; homogeneity; standard simplex; normal form; term function; discrete Sugeno integral; Lattice polynomial function
Showing items related by title and author.