Hyperstructures are algebraic structures equipped with at least one multi-valued operation, called a hyperoperation. The largest classes of the hyperstructures are the ones called – structures. A hyperoperation on a nonempty set is a mapping from to the nonempty power set , meaning the set of all nonempty subsets of , i.e. For we define and is a semihypergroup if is an associative hyperoperation, i.e. for all Furthermore, a hypergroup is a semihypergroup , where the reproduction axiom is valid, i.e. for all References AHA (Algebraic Hyperstructures & Applications). A scientific group at Democritus University of Thrace, School of Education, Greece. aha.eled.duth.gr Applications of Hyperstructure Theory, Piergiulio Corsini, Violeta Leoreanu, Springer, 2003, , Functional Equations on Hypergroups, László, Székelyhidi, World Scientific Publishing, 2012, Abstract algebra