On the Distributivity Equation I(x,u_1(y,z)) = u_2(I(x,y),I(x,z)) for Decomposable Uninorms (in Interval-Valued Fuzzy Sets Theory) Generated from Conjunctive Representable Uninorms

摘要

In this paper we continue investigations connected with distributivity of implication operations over decomposable (t-representable) operations. Our main goal is to show the general method of solving the following distributivity equation I(x,u_1(y, z)) = u_2(I(x, y), I(x, z)), when u_1, u_2 are decomposable uninorms (in interval-valued fuzzy sets theory) generated from two conjunctive representable uninorms. As a byproduct result we show all solutions of some functional equation related to this case.