In this paper, the notion of (L, M)- fuzzy convex derived hull spaces is introduced. It is proved that the category of (L, M)- fuzzy convex derived hull spaces is isomorphic to the category of (L, M)- fuzzy convex spaces and the category of (L, M)- fuzzy convex enclosed relation spaces. Based on this, the notion of (L, M)- fuzzy restricted convex derived hull spaces is introduced. It is further proved that the category of (L, M)- fuzzy restricted convex derived hull spaces is isomorphic to the category of (L, M)- fuzzy restricted convex hull spaces.