New Fuzzy Rough Set Models Based on Implication OperatorsNew fuzzy rough set models based on implication operatorsX. Zhang et al.

被引：0

作者：

Xiaoyi Zhang ^{[1
]}

Qi Liu ^{[1
]}

Chao Zhang ^{[2
]}

Jianming Zhan ^{[1
]}

机构：

[1] Hubei Minzu University,School of Mathematics and Statistics

[2] Shanxi University,Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology

来源：

Computational and Applied Mathematics | 2025年 / 44卷 / 3期

关键词：

Fuzzy ; -covering approximation space; -implication operator; Fuzzy rough set; 03E72; 68P20;

D O I：

10.1007/s40314-025-03088-z

中图分类号：

学科分类号：

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 β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}-covering approximations (Fβ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document}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 β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} neighborhood operators, fuzzy β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} 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.

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