Scholarlink

<p>Fuzzy rough set (FRS) is an important mathematical tool for dealing with uncertain, imprecise data and complex data relationships. However, in the properties of most covering-based fuzzy rough set models, there is still a situation where the upper approximation does not contain the lower approximation. This problem reduces the classification accuracy of the model, and then results in the effectiveness of the model in decision support. Therefore, In the space of fuzzy <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3088_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-covering approximations (F<InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3088_Article_IEq2.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>CAS), a new model is introduced that ensures the upper approximation encompasses the lower approximation. This model is developed using fuzzy neighborhood operators combined with <i>R</i>-implication operators. Additionally, the FRS approach via eight distinct types of operators is explored: fuzzy <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3088_Article_IEq3.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> neighborhood operators, fuzzy <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40314_2025_3088_Article_IEq4.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\beta \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> complementary neighborhood operators, and the properties of these models are discussed. Finally, the practical implications of these models in real-world applications are assessed, taking all the mentioned models into consideration.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

New Fuzzy Rough Set Models Based on Implication Operators

  • 期刊论文

  • 发表日期：

    2025年1月16日

查看全文
  • Xiaoyi Zhang,
  • Qi Liu,
  • Chao Zhang,
  • Jianming Zhan

摘要

Fuzzy rough set (FRS) is an important mathematical tool for dealing with uncertain, imprecise data and complex data relationships. However, in the properties of most covering-based fuzzy rough set models, there is still a situation where the upper approximation does not contain the lower approximation. This problem reduces the classification accuracy of the model, and then results in the effectiveness of the model in decision support. Therefore, In the space of fuzzy \(\beta \) β -covering approximations (F \(\beta \) β CAS), a new model is introduced that ensures the upper approximation encompasses the lower approximation. This model is developed using fuzzy neighborhood operators combined with R-implication operators. Additionally, the FRS approach via eight distinct types of operators is explored: fuzzy \(\beta \) β neighborhood operators, fuzzy \(\beta \) β complementary neighborhood operators, and the properties of these models are discussed. Finally, the practical implications of these models in real-world applications are assessed, taking all the mentioned models into consideration.