Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy sets and fuzzy logic: the foundations of application—from a mathematical point of view
Fuzzy set theory—and its applications (3rd ed.)
Fuzzy set theory—and its applications (3rd ed.)
Pattern Recognition with Fuzzy Objective Function Algorithms
Pattern Recognition with Fuzzy Objective Function Algorithms
On the Mutual Definability of Fuzzy Tolerance Relations and Fuzzy Tolerance Coverings
ISMVL '95 Proceedings of the 25th International Symposium on Multiple-Valued Logic
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
On the Mutual Definability of Fuzzy Tolerance Relations and Fuzzy Tolerance Coverings
ISMVL '95 Proceedings of the 25th International Symposium on Multiple-Valued Logic
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Abstract: 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.