The category of double fuzzy preproximity spaces

In this paper, we introduce the notions of double neighborhood systems and double fuzzy preproximity in double fuzzy topological spaces. We used double neighborhoods to study the initial structure of double fuzzy topological spaces, and the joins between them and the initial structures of double fuzzy preproximity spaces. Furthermore, we have proved that the category of double fuzzy preproximity spaces is a topological category, and hence a topological construct.