Abstract
The aim of this paper is to introduce and study the notions of (L, M)-double fuzzy topological molecular lattice, (L, M)-double fuzzy remote neighborhood space, and to construct the category (L, M)-DFRN which contains (L, M)-TDFRN as a full subcategory. (L, M)-TDFRN is shown as an isomorphic with (L, M)-DFTML. Finally, the notion of (L, M)-double fuzzy ideal was introduced and the theory of (L, M)-double fuzzy ideal convergence in an (L, M)-double fuzzy topological molecular lattice was established.