Ordered gamma nearness semigroups

Abstract Near set theory, which is a generalization of rough set theory, is based on the determination of universal sets according to the available information of the objects. In this paper, we state the way of defining ordered $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> -nearness semigroups. Moreover, we show how to transfer properties of ordered $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> -semigroups to ordered $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> -semigroups on weak nearness approximation spaces. For this, we define ordered $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> -nearness semigroups, $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> -nearness ideals and explore some properties. Also, we give examples for them.