n-hypergroups and binary relations

In this paper, we introduce and study the notion of a partial n-hypergroupoid, associated with a binary relation. Some important results concerning Rosenberg partial hypergroupoids, induced by relations, are generalized to the case of n-hypergroupoids. Then, n-hypergroups associated with union, intersection, products of relations and also mutually associative n-hypergroupoids are analyzed. Finally, n-hypergroupoids associated with relations are used in order to Study the transitivity of the relation beta in n-semihypergroups. (c) 2007 Elsevier Ltd. All rights reserved.