Pseudo-polynomial functions over finite distributive lattices

• Authors: Miguel Couceiro;Tamás Waldhauser
• Venue: ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
• Year: 2011

In this paper we extend the authors' previous works [6,7] by considering an aggregation model f : X1 × . . . × Xn → Y for arbitrary sets X1, . . . , Xn and a finite distributive lattice Y, factorizable as f(x1, . . . , xn) = p(ϕ1(x1), . . . , ϕn(xn)), where p is an n-variable lattice polynomial function over Y, and each ϕk is a map from Xk 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.