About some join spaces and hyperlattices

The aim of this paper is to construct some join spaces and hyperlattices. Suppose s is a function from G into P * (X). We define a hyperoperation s on the set G by, a s b = {g E G s(g) < s(a) U s(b)} and prove that if the image G is a V-subsemilattice of G or constitute a partition of X, then (G, s * ) is a hypergroup. Next we consider the set of all sub-hypergroups of this hypergroup and define a hyperlattice structure on this set.