A class of semihypergroups connected to preordered weak ΓΓ-semigroups

We introduce the concept of weak ΓΓ-semigroups as a generalization of ΓΓ-semigroups. Using preordered weak ΓΓ-semigroups, we obtain a class of semihypergroups and we analyze them in this paper. A connection between morphisms of semihypergroups associated with preordered ΓΓ-semigroups and morphisms of preordered structures is also investigated.