Abstract

In this paper, the main goal is to study an ordered Γ-semihypergroup H in the context of the characterizations of the associated Γ-semihypergroup B(H) of all bi-Γ-hyperideals of H. We show that an ordered Γ-semihypergroup H is a Clifford ordered Γ-semihypergroup if and only if B(H) is a semilattice. We also show that a Γsemihypergroup B(H) is a normal band if and only if the ordered Γ-semihypergroup H is simultaneously regular and intra regular. Furthermore, for each subclass S with many bands, we prove that for an ordered Γ-semihypergroup H, the conditional inclusion B(H) ∈ S holds true.