Hypergroups and nn-ary relations

In this paper we associate a hypergroupoid 〈H,⊗ρ〉〈H,⊗ρ〉 with an nn-ary relation ρρ defined on a nonempty set HH. We investigate when it is an HvHv-group, a hypergroup or a join space. Then we determine some connections between this hypergroupoid and Rosenberg’s hypergroupoid associated with a binary relation.