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.