some ordered hypersemigroups which enter their properties into their σ-classes

An important problem in the theory of ordered hypersemigroups is to describe the ordered hypersemigroups which enter their properties into their sigma;-classes. in this respect, we prove the following: if h is a regular, left (right) regular, completely regular, intra-regular, left (right) quasi-regular, semisimple, k regular, archimedean, weakly commutative, left (right) simple, simple, left (right) strongly simple ordered semigroup and sigma; a complete semilattice congruence on h then, for each a isin; h, the sigma;-class (a) sigma; of h is, respectively, so.