In this paper, the notion of direct sum of a family of convex spaces is generalized to that of a family of (L, M)-fuzzy convex spaces. Firstly, the related properties between the direct sum of a family of (L, M)-convex spaces and its factor spaces are discussed. Secondly, the (L, M)-fuzzy direct sum convex spaces are characterized by means of its some level L-direct sum convex spaces. Finally, the additivity of separabili...
