M-FUZZIFYING INTERVAL SPACES

In this paper, we introduce the notion of $M$-fuzzifying interval spaces, and discuss the relationship between $M$-fuzzifying interval spaces and $M$-fuzzifying convex structures.
It is proved that the category {\bf MYCSA2} can be embedded in the category {\bf MYIS} as a reflective subcategory, where {\bf MYCSA2} and {\bf MYIS} denote the category of $M$-fuzzifying convex structures of $M$-fuzzifying arity $\leq 2$ and the category of $M$-fuzzifying interval spaces, respectively.
Under the framework of $M$-fuzzifying interval spaces, subspaces and product spaces are presented and some of their fundamental properties are obtained.