Affiliations: Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan | Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia | Department of Mathematics, College of Science in Al-Zulfi, Majmaah University, Al-Zulfi, Saudi Arabia
Note: [] Corresponding author. Naveed Yaqoob, Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan. E-mail: [email protected]
Abstract: The combination of rough set theory and algebraic systems provide more new interesting research topics, which have drawn attention of many mathematicians and computer scientists. In this paper, we study the roughness of sub Γ-semihypergroups, Γ-hyperideals and bi-Γ-hyperideals in terms of set valued homomorphisms. We applied generalized lower and upper approximation operators to Γ-semihypergroups. We proved that the generalized lower and upper approximations of a Γ-hyperideal, by mean of a set valued mapping, is a Γ-hyperideal which is an extended notion of rough Γ-hyperideals introduced in [11]. Also we introduced the notion of generalized rough M-hypersystems and generalized rough N-hypersystems in Γ-semihypergroups and proved that the generalized upper rough approximation of an M-hypersystem (resp., N-hypersystem) is an M-hypersystem (resp., N-hypersystem).
