The paper deals with the connection of fuzzy sets and of join spaces with a hypergroupoid. For the last connection, introduced by Corsini in 2003, the second author obtained some results in 2007. In this paper the authors continue to obtain results in this direction. The main result is: Consider a sequence of fuzzy sets and join spaces associated with a hypergroupoid then a sufficient condition in order to have non-isomorphic consecutive associated join spaces is proved. A second result is that they present a necessary and sufficient condition for a join space in the sequence to be a reduced hypergroup.