Fuzzy equivalence relations and their equivalence classes

In this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice. We give certain characterizations of fuzzy semi-partitions and fuzzy partitions over a complete residuated lattice, as well as over a linearly ordered complete Heyting algebra. In the latter case, for a fuzzy equivalence relation over a linearly ordered complete Heyting algebra, we construct an algorithm for calculation of a minimal family of its equivalence classes which generates it. Most of the presented results are new, but some of them are generalizations of known results given in a way which simplifies and clarifies them.