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

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.