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In this paper, we introduce the concepts of fuzzifying topological interiors, fuzzifying topological closures and fuzzifying topological limit structures. A comprehensive characterization theorem about fuzzifying topological interiors are proved. Characterizations of fuzzifying topologies by filter convergence structures are given.

We show that every topological fuzzy neighborhood convergence space is a fuzzy neighborhood space. Consequently, the meet of the categories FNCS and FTS is the category FNS.

The main purpose of this paper is to prove that there exist interesting alternative characterizations of the category FNCS introduced by Blasco and Lowen (Fuzzy Sets and Systems 76 (3) (1995) 395–406); e.g., the category FYPS of fuzzifying pretopological spaces and continuous maps. Some new results about fuzzy neighborhood convergence spaces are also obtained.

The main result in this paper is that the category of fuzzy neighborhood spaces is isomorphic to that of fuzzifying topological spaces.