ON GENERALIZED ROUGH (m, n)-BI-Γ-HYPERIDEALS IN Γ-SEMIHYPERGROUPS

Abstract

Recently, in [12], Yaqoob et al. introduced the notion of (m,n)-bi-Gamma-hyperideals and applied the concept of rough set theory to (m,n)-bi-Gamma-hyperideals, which is a generalization of (m,n)-bi-Gamma-hyperideals of Gamma-semihypergroups. In this paper, applying the rough set theory based on an arbitrary binary relation (not an equivalent relation) we extend and generalize these notions, introducing the notion of generalized rough (m,0)-Gamma-hyperideals (generalized rough (0, n)-Gamma-hyperideals), generalized rough (m, n)-quasi and bi-Gamma-hyperideals and generalized rough m-left Gamma-hyperideals) and establish some of their basic properties in Gamma-semihypergroups.