Abstract
It is well known that if (S,∘) is a semihypergroup and ρ is a strongly regular relation on S, then S/ρ, the set of equivalence classes, is a semigroup with the binary operation: ρ(x)⊙ρ(y)=ρ(z) for all z∈x∘y. Now, let (S,∘,≤) be an ordered semihypergroup. The following question is natural: Is there a strongly regular relation ρ on S for which S/ρ is an ordered semigroup? One of our main aim in this paper is reply to the above question. Then, we study some properties and isomorphisms between them.
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