The structures of intuitionistic fuzzy equivalence relations

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 αα-cut relations of intuitionistic fuzzy equivalence relations. We investigate the chain structure and the partially ordered structure of αα-cut relations of intuitionistic fuzzy equivalence relations. We also show that the intuitionistic fuzzy equivalence relations can be applied for clustering analysis.