<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11587_2025_948_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\Gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation>-nearness semigroups. Moreover, we show how to transfer properties of ordered <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11587_2025_948_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\Gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation>-semigroups to ordered <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11587_2025_948_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\Gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation>-semigroups on weak nearness approximation spaces. For this, we define ordered <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11587_2025_948_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\Gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation>-nearness semigroups, <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11587_2025_948_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">$\Gamma $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Γ</mi> </math></EquationSource> </InlineEquation>-nearness ideals and explore some properties. Also, we give examples for them.</p>

Ordered gamma nearness semigroups

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2025年3月13日

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Özlem Tekin,
Mehmet Ali Öztürk

摘要

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 $ $Γ$ -nearness semigroups. Moreover, we show how to transfer properties of ordered $\Gamma $ $Γ$ -semigroups to ordered $\Gamma $ $Γ$ -semigroups on weak nearness approximation spaces. For this, we define ordered $\Gamma $ $Γ$ -nearness semigroups, $\Gamma $ $Γ$ -nearness ideals and explore some properties. Also, we give examples for them.