Intuitionistic fuzzy sets and join spaces associated with ary membership functions

In this paper, we associate finite hyperstructures with fuzzy sets endowed with n ? ary membership functions and analyze the properties of this new hyperstructures. We prove that the new hyperstructure is a commutative hypergroup, but generally it is not a join space. We give some conditions such that the hypergroup has this property. In particular, we investigate some natural equivalence relations on the set of all intuitionistic fuzzy sub-hypergroups of a hypergroup.