nn-hypergroups and binary relations

In this paper, we introduce and study the notion of a partial nn-hypergroupoid, associated with a binary relation. Some important results concerning Rosenberg partial hypergroupoids, induced by relations, are generalized to the case of nn-hypergroupoids. Then, nn-hypergroups associated with union, intersection, products of relations and also mutually associative nn-hypergroupoids are analyzed. Finally, nn-hypergroupoids associated with relations are used in order to study the transitivity of the relation ββ in nn-semihypergroups.