On the equivalence of two symmetric differences

Abstract

We study two models of symmetric difference of two fuzzy sets. In fuzzy logic we call this exclusive or operator. We show that in the Pliant operator case, the natural extensions of two expressions are equivalent. It was an interesting open problem to determine (independently of the definition of symmetric difference) for which t-norms and t-conorms and strong negations of two variables are associative operations on the unit interval. Here, in this article we show that the Pliant operators have this property.