Ordered regular equivalence relations on ordered semihypergroups

In this paper, we introduce the concept of ordered regular (strongly ordered regular) equivalence relation on an ordered semihypergroup. Moreover, we use hyperfilters to construct a strongly ordered regular equivalence relation on an ordered semihypergroup, for which the corresponding quotient structure is a semilattice. Finally, we construct an ordered regular equivalence relation on an ordered semihypergroup by hyperideals such that the corresponding quotient structure is also an ordered semihypergroup under a related order relation, which is an answer to the open problem given by B. Davvaz, P. Corsini and T. Changphas in European Journal of Combinatorics.