In this paper, the notion of (L, M)-fuzzy topological-convex spaces is introduced and some of its characterizations are obtained. Then the notion of (L, M)-fuzzy convex enclosed relation spaces is introduced and its one-to-one correspondence with (L, M)-fuzzy convex space is studied. Based on this, the notion of (L, M)-fuzzy topological-convex enclosed relation spaces is introduced and its categorical isomorphism to (L, M)-fuzzy topological-convex spaces is discussed