Equivalence operators that are associative

We begin with a paradox of the equivalence relation, and we solve it by using the neutral value of the negation. The so-called Pliant equivalence operator fulfils the modified requirements of the fuzzy equivalence relations. After, we study two models of the equivalence operator. We show that in the Pliant operator case the natural extension of two expressions is equivalent. It has two different types of transitivity. It is associative, and it can be extended to many variables. On this basis, we can create the weighted form of the equivalence operator.