Prime (m,n) Bi-Γ-Hyperideals in Γ-Semihypergroups

Relations between rough sets and algebraic structures have been already considered by many mathematicians. Motivated by studying the properties of rough (m,n) bi-Gamma-hyperideals in Gamma-semihypergroups, we now introduced the notion of prime (m,n) bi-Gamma--hyperideals in Gamma-semihypergroups and investigated several properties of these prime (m,n) bi-Gamma-hyperideals. Also we applied the rough set theory to these prime (m,n) bi-Gamma-hyperideals and proved that the lower and upper approximation of a prime (m,n) bi-Gamma-hyperideal is a prime (m,n) bi-Gamma-hyperideal in a Gamma-semihypergroup. In the end we established some results on rough prime (m,n) bi-Gamma-hyperideals in the quotient Gamma-semihypergroups.