New categories of coverings in terms of rough fuzzy sets

IF 2.6 3区数学 Computational and Applied Mathematics Pub Date : 2024-08-19 DOI:10.1007/s40314-024-02882-5

Mohammed Atef

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Abstract

In this article, we develop innovative models of multigranulation rough fuzzy sets, utilizing fuzzy \(\beta \)-covering and incorporating a range of techniques such as fuzzy \(\beta \)-neighborhood, fuzzy complementary \(\beta \)-neighborhood, fuzzy \(\beta \)-minimal description, and fuzzy \(\beta \)-maximal description. The axiomatic characteristics of fuzzy \(\beta \)-neighborhoods within the context of fuzzy \(\beta \)-covering based multigranulation rough fuzzy sets (F\(\beta \)CMGRFS) are analyzed. Thus, we introduce seven new classes of F\(\beta \)CMGRFS and investigate their relevant properties. Furthermore, the connections and associations between these techniques are established. Thus, we provide a set of observations and propositions that highlight the value and dissimilarities of our proposed models compared to others. A test example is produced to verify the applicability of the presented strategies and treat MCGDM issues. Finally, we compare the outcomes of our approaches and the existing studies to check the reliability and the validity of our work.

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用粗糙模糊集表示覆盖的新类别

在本文中，我们利用模糊（beta）覆盖并结合一系列技术，如模糊（beta）邻域、模糊互补（beta）邻域、模糊（beta）最小描述和模糊（beta）最大描述，建立了多粒度粗糙模糊集的创新模型。在基于模糊（beta）覆盖的多粒度粗糙模糊集（F（beta）CMGRFS）的背景下，分析了模糊（beta）邻域的公理特征。因此，我们引入了七类新的 F\(\beta\)CMGRFS 并研究了它们的相关性质。此外，我们还建立了这些技术之间的联系和关联。因此，我们提出了一系列意见和主张，强调了我们提出的模型与其他模型相比的价值和不同之处。我们还制作了一个测试示例，以验证所提出策略的适用性并处理 MCGDM 问题。最后，我们比较了我们的方法和现有研究的结果，以检验我们工作的可靠性和有效性。

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来源期刊

Computational and Applied Mathematics MATHEMATICS, APPLIED-

自引率

11.50%

发文量

352

期刊介绍： Computational & Applied Mathematics began to be published in 1981. This journal was conceived as the main scientific publication of SBMAC (Brazilian Society of Computational and Applied Mathematics). The objective of the journal is the publication of original research in Applied and Computational Mathematics, with interfaces in Physics, Engineering, Chemistry, Biology, Operations Research, Statistics, Social Sciences and Economy. The journal has the usual quality standards of scientific international journals and we aim high level of contributions in terms of originality, depth and relevance.