Hyperstructures and fuzzy sets endowed with two membership functions

This paper contains new results concerning finite hyperstructures associated with fuzzy sets endowed with two membership functions. In general, these hyperstructures are commutative hypergroups, but not join spaces. We give some conditions such that the considered hypergroups have also this property and we present examples of their fuzzy subhypergroups. Then we analyze two sequences of join spaces and fuzzy sets associated with a finite hypergroupoid, using fuzzy sets endowed with two membership functions.