I-fuzzy topological groups

In this paper, the concept of I-fuzzy topological groups is introduced and some of its properties are discussed. Considering Jin-ming Fangʹs notion of I-fuzzy quasi-coincident neighborhood system [Fuzzy Sets and Systems 147 (2004) 317–325], we obtained a characterization of I-fuzzy topological groups in terms of the corresponding I-fuzzy quasi-coincident neighborhood system at identity element. Finally, we showed that the category of I-fuzzy topological groups and fuzzy continuous homomorphisms is isomorphic to the category of antichain I-topological groups and I-continuous homomorphisms; and the category I-fuzzy topological groups is topological over the category of groups with respect to the forgetful functor.