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.