On a Class of Distributive Fuzzy Implications

Abstract

We deal with the system of functional equations I(x,T(y,z))=T(I(x,y), I(x,z)), I(x,I(y,z))=I(T(x,y),z), where function T:[0,1]²→ [0,1] is a strict t-norm and I:[0,1]²→ [0,1] is an unknown function. Under some assumptions imposed on function I we obtain that I is almost conjugate with the Yager fuzzy implication.