semihypergroups that every hyperproduct only contains some of the factors

Breakable semihypergroups, defined by a simple property: every non-empty subset of them is a subsemihypergroup. in this paper, we introduce a class of semihypergroups, in which every hyperproduct of n elements is equal to a subset of the factors, called πn-semihypergroups. then, we prove that every semihypergroup of type π2k, (k ≥ 2) is breakable and every semihypergroup of type π2k+1 is of type π3. furthermore, we obtain a decomposition of a semihypergroup of type πn into the cyclic group of order 2 and a breakable semihypergroup. finally, we give a characterization of semi-symmetric semihypergroups of type πn.