This paper investigates the lattice structure of the collections of (r, s)-regular fuzzy closed sets and (r, s)-regular fuzzy open sets in a double fuzzy topological space. They are shown to be join semi-lattice and meet semi-lattice, respectively, and their intersection is a modular lattice. Moreover, the collection of all such lattices forms a distributive lattice.

double fuzzy topological space, regular fuzzy closed, regular fuzzy open, lattice.