The main purpose of this paper is to extend the concepts of left and right
bases in Γ-semigroups which had been introduced by Changphas and Kummoon in 2018.
In this paper, we introduce the concepts of left and right bases of ordered Γ-semihypergroups and extend the results in Γ-semigroups to ordered Γ-semihypergroups. In addition,
we investigate the structure of an ordered Γ-semihypergroup containing the right bases.
We prove that all of the right bases of an ordered Γ-semihypergroup have the same cardinality. Furthermore, we also prove that an ordered Γ-semihypergroup eliminating the
union of all right bases, if it is non-empty, is a left Γ-hyperideal of such ordered Γsemihypergroup.