A note on congruence permutability and fuzzy logic

We study congruence permutability of algebras with fuzzy equalities. The notion of degree of congruence permutability naturally arises in this context. We present a Mal'cev-like characterization of congruence permutable varieties of algebras with fuzzy equalities. Our note presents a way to generalize various congruence conditions from the point of view of fuzzy logic.