Abstract
In this paper, we introduce the concept of prime bi-Gamma-hyperideals, rough prime bi-Gamma-hyperideals and fuzzy prime bi-Gamma-hyperideals of Gamma-semihypergroups. We prove that the lower approximation of a prime bi-Gamma-hyperideal is a prime bi-Gamma-hyperideal and the upper approximation of a prime bi-Gamma-hyperideal is a prime bi-Gamma-hyperideal. Also the rough set theory is applied to prime bi-Gamma-hyperideals in the quotient Gamma-semihypergroups. In the end, the notion of fuzzy prime bi-Gamma-hyperideals of Gamma-semihypergroups has been introduced, and we proved that a bi-Gamma-hyperideal B of a Gamma-semihypergroup H is prime (resp., strongly prime) if and only if the characteristic function X-B of B is a fuzzy prime (resp., fuzzy strongly prime) bi-Gamma-hyperideal of H.