This paper proposes a reflexive fuzzy $\beta$-neighborhood operator by modifying Ma’s fuzzy $\beta$-neighborhood operators. Then, we use such an operator to build a covering-based variable precision fuzzy rough set (CVPFRS) model that can deal with the issue of misclassifications and perturbations in decision-making problems. By combining the CVPFRS model with two traditional decision-making methods (the PROMETHE method and the DEAS method), we introduce a novel method for addressing multi-attribute decision-making (MADM) problems. An illustrative example is utilized to demonstrate the practicality of the proposed method. The effectiveness of the proposed method is validated by comparing it with existing methods. By virtue of the cross-validation and hypothesis testing, we give an experimental analysis to interpret the validity and stability of the proposed method.

本文提出了一种自反模糊 $\beta$马氏模糊修正的近邻算子 $\beta$-邻里运营商。然后，我们使用这种算子来构建基于覆盖的可变精度模糊粗糙集（CVPFRS）模型，该模型可以处理决策问题中的错误分类和扰动问题。通过将CVPFRS模型与两种传统的决策方法（PROMETHE方法和DEAS方法）相结合，我们介绍了一种解决多属性决策（MADM）问题的新方法。利用一个说明性的例子来证明所提出方法的实用性。通过与现有方法进行比较验证了所提方法的有效性。通过交叉验证和假设检验，我们进行了实验分析以解释所提出方法的有效性和稳定性。