On the disjoint sums of M-fuzzifying convex spaces

Abstract

In this paper, we first extend the concept of the arity in crisp convex spaces to the case of fuzzification and give some related properties. From the view of arity and hull operator, we study the relations between the disjoint sum of M-fuzzifying convex spaces and its factor spaces. We also examine the additivity of the degree of separability (S0; S1; S2; S3; S4). Finally, we show that every factor space is
M-fuzzifying JHC iff the corresponding disjoint sum space is JHC.