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 @b in n-semihypergroups.
['V. Leoreanu-Fotea', 'Bijan Davvaz']
n-hypergroups and binary relations