On lattice-isomorphism between fuzzy equivalence relations and fuzzy partitions

We present our results concerning the fact that fuzzy equivalence relations and fuzzy partitions together with appropriate partial orderings form lattices and that these lattices are isomorphic. In our investigation we apply the results of H. Thiele, N. Schmechel (1995) concerning the definitions of fuzzy equivalence relations, fuzzy partitions and the existence of a bijection between them. We show that this bijection is a lattice isomorphism.