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 MYCSA۲}  can be embedded in  the category  {\bf  MYIS}  as a reflective subcategory, where  {\bf MYCSA۲} and   {\bf  MYIS} denote  the category of M-fuzzifying convex structures of  M-fuzzifying  arity \leq ۲  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.

Keywords:

M-fuzzifying interval spaces , M-fuzzifying convex structures , M-fuzzifying interval preserving functions , Subspaces , Product spaces