-hypergroups and binary relations

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