On the fuzzy grade of hypergroups

In some previous papers, the second author studied the possibility to associate a sequence of membership functions and of join spaces with a hypergroupoid H. Here we establish a sufficient condition in order to have two consecutive associated join spaces iH and i+1H non-isomorphic. We find also a property of the quotient hypergroup determined by the join space iH and the relation associated with the fuzzy set and finally, we determine a necessary and sufficient condition for the join space iH in order to be a reduced hypergroup.