现实场景中普遍存在模糊性数据，针对这类具有不确定性的数据，传统统计方法往 往难以有效提取所需信息。在此背景下，模糊理论因其在处理不确定性信息方面的独特 优势应运而生。稳健模糊回归是模糊分析的重要基础，它在处理模糊数据的同时，还能 抑制数据中的异常值对参数估计结果的影响，提高模型的稳健性。但现有的稳健模糊估 计方法无法同时满足最高崩溃污染率和有效性。因此，本文将经典参数估计方法 REWLS 引入到模糊领域，提出了一种新的稳健模糊估计方法——FREWLS。

首先，本文回顾了模糊理论中的基本概念，介绍了模糊理论中的模糊集和模糊数等 基础概念和模糊回归模型现有的几种参数估计方法。

其次，结合模糊理论和经典稳健估计方法具体构建 FREWLS，对提出方法的核心原 理及算法作了详细的阐述和证明。通过均方根误差等四种评估指标定义了模型的综合得 分函数，构建了多维数据场景（包括数据维度和异常值的类型与比例），通过数值模拟 研究，首先选出最优初始估计作为对比基础，继而将 FREWLS 估计与 FLS 等四种模糊 回归方法进行多维度比较，在理论证明和数值模拟两个层面验证了所提方法的有效性。

再次，提出基于稳健马氏距离和 FREWLS 结合的异常值检测方法。本方法主要分为 两个阶段：第一阶段基于 FREWLS 计算均值和协方差；第二阶段根据稳健马氏距离判断 异常值。为评估异常值检测方法的性能，本文引入识别率等三个评估指标，使用数值模 拟方法对两个方面进行验证：一是不同维度回归模型下的异常值检测方法性能；二是不同异常值比例场景下的方法性能。本文将所提方法与基于 MCD 和 MVE 的稳健马氏距 离与进行对比分析，结果表明本文所提方法的性能更好。

最后，通过实例分析来进一步验证本文所提方法的有效性和应用价值。本文选取两 个实例，分别为空气质量指数预测和电力负荷预测。为了保证实例的可靠性，首先使用 提出的异常值检测方法对两组数据进行识别。然后使用 FREWLS 拟合数据，结果表明， 相较于其他三种模糊回归方法，FREWLS 的估计效果更好。

Real-world scenarios often involve ambiguous data, and traditional statistical methods struggle to effectively extract desired information from such uncertain data. In this context, fuzzy theory has emerged due to its unique advantages in handling uncertain information.

Robust fuzzy regression, a fundamental component of fuzzy analysis, not only processes fuzzy data but also mitigates the impact of outliers on parameter estimation, enhancing model robustness. However, The existing robust fuzzy estimation methods fail to satisfy both the maximum breakdown contamination rate and effectiveness simultaneously. To address this, this paper introduces the classical parameter estimation method REWLS into the fuzzy domain, proposing a novel robust fuzzy estimation method—FREWLS.

First, this paper reviews basic concepts in fuzzy theory, including fuzzy sets and fuzzy numbers, and introduces existing parameter estimation methods for fuzzy regression models.

Second, we construct FREWLS by integrating fuzzy theory with classical robust estimation methods, providing detailed explanations and proofs of its core principles and algorithms. Using four evaluation metrics, including root mean square error, we define a comprehensive score function for the model. Multidimensional data scenarios (covering data dimensions and outlier types/proportions) are constructed, Through numerical simulation studies, we first selected the optimal initial estimation method as a benchmark , followed by a multidimensional comparative analysis between FREWLS and four fuzzy regression methods including FLS. The effectiveness of the proposed method was validated at both theoretical and empirical levels.

Third, we propose an outlier detection method combining robust Mahalanobis distance with FREWLS. This method operates in two stages: Stage 1 computes the mean and covariance based on FREWLS, while Stage 2 identifies outliers using robust Mahalanobis distance. To evaluate performance, three metrics are introduced. Numerical simulations verify two aspects:

(1) the method’s performance under regression models of varying dimensions; and (2) its performance under different outlier proportions. Comparisons with robust Mahalanobis distance methods based on MCD and MVE demonstrate the superiority of the proposed method.

Finally, case studies further validate the effectiveness and applicability of the proposed method. Two instances are analyzed: air quality index prediction and electric load prediction.

To ensure reliability, the proposed outlier detection method is first applied to both datasets. Subsequent fitting with FREWLS shows superior estimation performance compared to three  other fuzzy regression methods.

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