Pseudo-polynomial functions over finite distributive lattices

Waldhauser, Tamás; Couceiro, Miguel

Waldhauser, Tamás; Couceiro, Miguel (2014), Pseudo-polynomial functions over finite distributive lattices, Fuzzy Sets and Systems, 239, p. 21-34. http://dx.doi.org/10.1016/j.fss.2012.09.007

Type

Article accepté pour publication ou publié

External document link

http://arxiv.org/abs/1110.1811

Date

2014

Journal name

Fuzzy Sets and Systems

Volume

239

Publisher

Elsevier

Pages

21-34

Abstract (EN)

In this paper we consider an aggregation model f: X1 x ... x Xn --> Y for arbitrary sets X1, ..., Xn and a finite distributive lattice Y, factorizable as f(x1, ..., xn) = p(u1(x1), ..., un(xn)), where p is an n-variable lattice polynomial function over Y, and each uk is a map from Xk to Y. The resulting functions are referred to as pseudo-polynomial functions. We present an axiomatization for this class of pseudo-polynomial functions which differs from the previous ones both in flavour and nature, and develop general tools which are then used to obtain all possible such factorizations of a given pseudo-polynomial function.

Subjects / Keywords

Sugeno integral; distributive lattice; lattice polynomial function; pseudo-polynomial function; axiomatization; factorization; multicriteria decision making