### Roughness Applied to Generalized \(\Gamma\)-ideals of Ordered LA \(\Gamma\)-Semigroups

#### Abstract

In this paper, we have applied rough set theory to generalized ordered \(\Gamma\)-ideals in ordered LA \(\Gamma\)-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-\(\Gamma\)-semigroups and have shown that lower and upper approximations of an LA-\(\Gamma\)-subsemigroups (resp., left ideals, right ideals, interior ideals, two-sided ideals, quasi-ideals, bi-ideals and prime ideals) in an ordered LA-\(\Gamma\)-semigroup is an LA-\(\Gamma\) subsemigroups (resp., left ideals, right ideals, interior ideals, two-sided ideals, quasi-ideals, bi-ideals and prime ideals).

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