Semihypergroup actions by using the generalized permutations

An ordered hypergroupoid is a hypergroupoid together with a partial order such that satisfies the monotone condition. In this paper, we introduce the notion of semihypergroup actions on ordered hypergroupoids. Some results in this respect are investigated. In particular, we prove that if S is a commutative semihypergroup acting on an ordered hypergroupoid H, then there exists a commutative semihypergroup S acting on the ordered hypergroupoid H: = (H S) / in such a way that H is embedded in H.