On direct sums of (L,M)-fuzzy convex spaces

Abstract

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 ofseparability (S−1, sub-S0, S0, S1, S2) are investigated.