<p>Given the concept of bipolar intuitionistic fuzzy set and a set <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1319_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega ,$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Ω</mi> <mo>,</mo> </mrow> </math></EquationSource> </InlineEquation> The concept of a bipolar intuitionistic <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1319_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>-fuzzy right (left) ideal, a bipolar intuitionistic <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1319_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>-fuzzy bi-ideals and a bipolar intuitionistic <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1319_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>-fuzzy ideal, a bipolar (1, 2)-ideals in semigroup are discussed and some results and properties are introduced. Using bipolar intuitionistic fuzzy bi-ideal, a bipolar intuitionistic <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13370_2025_1319_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">$\Omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">Ω</mi> </math></EquationSource> </InlineEquation>-fuzzy bi-ideals constructed. We discuss some theorems and properties on their concepts and some results are explored.</p>

Some properties in bipolar intuitionistic $\Omega $-fuzzy ideals over semigroups

期刊论文
发表日期：

2025年5月5日

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Mourad Oqla Massa’deh,
Ahlam Fellatah

摘要

Given the concept of bipolar intuitionistic fuzzy set and a set $\Omega ,$ $Ω,$ The concept of a bipolar intuitionistic $\Omega $ $Ω$ -fuzzy right (left) ideal, a bipolar intuitionistic $\Omega $ $Ω$ -fuzzy bi-ideals and a bipolar intuitionistic $\Omega $ $Ω$ -fuzzy ideal, a bipolar (1, 2)-ideals in semigroup are discussed and some results and properties are introduced. Using bipolar intuitionistic fuzzy bi-ideal, a bipolar intuitionistic $\Omega $ $Ω$ -fuzzy bi-ideals constructed. We discuss some theorems and properties on their concepts and some results are explored.

Some properties in bipolar intuitionistic \(\Omega \)-fuzzy ideals over semigroups

摘要