Document Type : Research Paper


1 College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610000, P.R. China

2 chool of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R. China


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.


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