New types of approximations via $\circledast$-$\beta$-soft fuzzy complement neighborhood and $\circledcirc$-$\beta$-soft fuzzy complement neighborhood and their applications in multiple attribute decision-making (MADM)

Khalil, Ahmed; Li, Shenggang; Yang, Hai-Long

doi:10.22111/ijfs.2025.50036.8834

Document Type : Research Paper

Authors

¹ Al-Azhar University

² College of Mathematics and Information Science, Shaanxi Normal University, 710062, Xian, P. R. China

³ Shaanxi Normal University China

https://doi.org/10.22111/ijfs.2025.50036.8834

Abstract

A $\beta$-soft fuzzy complement neighborhood is the initial concept proposed by Zhang and Zhan (International Journal of Machine Learning and Cybernetics 10(2019) 1487-1502), which we will refer to in this study as $\circledast$-$\beta$- soft fuzzy complement neighborhood. In the present paper, we first introduce three new approximation types based on $\beta$-soft fuzzy covering via $\circledast$-$\beta$-soft fuzzy complement neighborhood, along with several essential features and examples. The new approximation types are significant because they satisfy the inclusion property (i.e., the upper approximation contains the lower approximation, which is one of the essential features of rough set models). In addition, we update some algorithms to a very easy-to-understand state. As a result, improved decision-making procedures will be observable and trustworthy in order to arrive at the optimal choice. Second, we offer a novel idea of $\circledcirc$-$\beta$-soft fuzzy complement neighborhood and then present three other new approximation types based on $\beta$-soft fuzzy covering via $\circledcirc$-$\beta$ soft fuzzy complement neighborhood, besides outlining some of its key characteristics and giving some examples. On the theoretical side, by using three other new approximations via $\circledcirc$-$\beta$-FCN${\mathscr A},$ we also study some basic fuzzy topology properties. Third, we use $\circledcirc$-$\beta$-FCN${\mathscr A}$ to construct a new method that can be applied to the MADM field. We illustrate this method using a real-world problem: a candidate seeking employment in a company. Finally, to demonstrate the advantages of the proposed work, we will compare our proposed method with published $\beta$-soft fuzzy MADM methods.

Keywords

Main Subjects

Soft/Rough sets

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New types of approximations via $\circledast$-$\beta$-soft fuzzy complement neighborhood and $\circledcirc$-$\beta$-soft fuzzy complement neighborhood and their applications in multiple attribute decision-making (MADM)

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Volume 22, Issue 1January and February 2025Pages 185-207

Volume 22, Issue 1
January and February 2025
Pages 185-207