Some solutions of functional equation $I(I(y,x), I(x,y))=I(x,y)$ involving fuzzy implications

Abstract

In this article, a functional equation(IE) involving fuzzy implications has been considered. Two different perspectives of this equation have been provided to realize its significance. As it is very difficult to find the solutions of (IE) in general, the investigation of solutions of (IE) is restricted to main families of fuzzy implications.