Pseudo-polynomial functions over finite distributive lattices

Details Pseudo-polynomial functions over finite distributive lattices Pseudo-polynomial functions over finite distributive lattices

2011-10-09

arxiv.org/abs/1110.1811v1

Mathematics

Rings and Algebras

16 pages, 2 figures

Scientific paper

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.

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