Abstract
First, we introduce the concept of intuitionistic fuzzy group con- gruence and we obtain the characterizations of intuitionistic fuzzy group con- gruences on an inverse semigroup and a T -pure semigroup, respectively. Also, we study some properties of intuitionistic fuzzy group congruence. Next, we introduce the notion of intuitionistic fuzzy semilattice congruence and we give the characterization of intuitionistic fuzzy semilattice congruence on a T -pure semigroup. Finally, we introduce the concept of intuitionistic fuzzy normal congruence and we prove that (IFNC(ES),\,_) is a complete lattice. And we find the greatest intuitionistic fuzzy normal congruence containing an in- tuitionistic fuzzy congruence on ES.
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