L, M-fuzzy topological groups

Following the idea of L-fuzzy neighborhood system as introduced by F.-G. Shi, and its generalization to L, M-fuzzy neighborhood systems, we introduce the notion of L, M-fuzzy topological group, and obtain various properties, including some results on quotient groups of L, M-fuzzy topological groups. We show that the category of L, M-fuzzy topological groups is topological over the category of groups with respect to the forgetful functor.