On bi–bases of Γ–semihypergroups

This paper focuses on the Γ–semihypergroups. Our goal seeks to find the conditions of sub–Γ–semihypergroup using bi–bases properties. We provide definitions and explain some properties of bi–bases in Γ– semihypergroups. The findings extend the results from bi–bases of Γ– semigroups. The findings demonstrate that if B is a bi–bases of a Γ– semihypergroup H; then, B is a sub–Γ–semihypergroup of H if and only if for any b, c ∈ B and γ ∈ Γ, b ∈ bγc or c ∈ bγc.