Roughness Applied to Generalized \(Γ\)-ideals of Ordered LA \(Γ\)-Semigroups - Ansari, Moin Akhtar (Communications in Mathematics and Applications, 2019)
In this paper, we have applied rough set theory to generalized ordered \(Γ\)-ideals in ordered LA \(Γ\)-semigroups by using a new type of relations called pseudoorder of relations. Based on this relation we have studied properties of rough ideals, rough interior ideals, rough quasi-ideals, rough bi-ideals and rough prime ideals in ordered LA-\(Γ\)-semigroups and have shown that lower and upper approximations of an LA-\(Γ\)-subsemigroups (resp., left ideals, right ideals, interior ideals, two-sided ideals, quasi-ideals, bi-ideals and prime ideals) in an ordered LA-\(Γ\)-semigroup is an LA-\(Γ\) subsemigroups (resp., left ideals, right ideals, interior ideals, two-sided ideals, quasi-ideals, bi-ideals and prime ideals).
Keywords: LA-\(Γ\)-semigroups; Rough sets; Rough (left; right; quasi; bi; prime and interior)-\(Γ\)-ideals