Abstract
In this paper, we investigate some structures of intuitionistic fuzzy equivalence relations. We show that the family of all intuitionistic fuzzy equivalence relations on the set X is a complete lattice. Unlike the chain structure of the cut relations of fuzzy equivalence relations, there are two ordered structures concerned with the α-cut relations of intuitionistic fuzzy equivalence relations. We investigate the chain structure and the partially ordered structure of α-cut relations of intuitionistic fuzzy equivalence relations. We also show that the intuitionistic fuzzy equivalence relations can be applied for clustering analysis.
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