3 research outputs found
Axiomatizations of quasi-polynomial functions on bounded chains
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
From discrete Sugeno integrals to generalized lattice polynomial functions: axiomatizations and representations (invited lecture)
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 present complete descriptions of 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 present further axiomatizations for this class both in terms of functional equations and natural relaxations of homogeneity and median decomposability
Quasi-polynomial functions on bounded chains
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 present complete descriptions of 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 quasipolynomial 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 decomposability. As noteworthy particular cases, we investigate those subclasses of quasi-term functions and quasi-weighted maximum and minimum functions, and present characterizations accordingly