Abstract
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.