T-equalities as fuzzy non-Archimedean metrics and Δ+-fuzzy equivalences of type S

The starting point of our approach is the remark that a fuzzy T-equality can be regarded as a fuzzy non-Archimedean metric. Accordingly, we propose a generalization of the notions of T-equivalence and T-equality, by replacing the numbers E(x,y) with generalized distribution functions. Thus, we introduce the concepts of fuzzy T-equivalence of type S and fuzzy T-equality of type S, where T is a Menger norm and S is an operation on the nonnegative extended reals. By using specific methods from probabilistic metric spaces theory, concrete formulas for generated metrics, slightly extending some similar results of De Baets and Mesiar, are also given.