Pseudo-polynomial Functions over Finite Distributive Lattices

Abstract

In this paper we extend the authors’ previous works [6,7] by considering an aggregation model $f\colon X_{1}\times\cdots\times X_{n}\rightarrow Y$ for arbitrary sets X ₁,…,X _n and a finite distributive lattice Y, factorizable as

$$ ~f(x_{1},\ldots,x_{n})=p(\varphi_{1}(x_{1}),\ldots,\varphi_{n}(x_{n})), $$

where p is an n-variable lattice polynomial function over Y, and each ϕ _k is a map from X _k to Y. Following the terminology of [6,7], these 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.