In this paper, a new method is proposed for estimating fuzzy regression models based on a novel robust support vector machines with exact predictors and fuzzy responses. For this purpose, a three-stage support vector machine algorithm was introduced based on a modified robust loss function. Some common goodness-of-fit criteria and a popular kernel were also employed to examine the performance of the proposed method in cases where the outliers occur in the data set. The effectiveness of the proposed method was illustrated through three numerical cases including a simulation study and two applied examples. The proposed method was also compared with several common fuzzy linear/nonlinear/nonparametric regression models. The numerical results clearly indicated that the proposed model is capable of providing accurate results in the cases involving data sets with or without outliers. Thus, the proposed fuzzy regression model can be successfully applied to improve the prediction accuracy and interpretability of the fuzzy regression models for real-life applications in the intelligence systems.

本文提出了一种基于具有精确预测因子和模糊响应的新型鲁棒支持向量机估计模糊回归模型的新方法。为此，引入了基于修正的鲁棒损失函数的三阶段支持向量机算法。在数据集中出现异常的情况下，还使用了一些通用的拟合优度准则和流行的内核来检验所提出方法的性能。通过三个数值案例，包括仿真研究和两个应用实例，说明了该方法的有效性。还将所提出的方法与几种常见的模糊线性/非线性/非参数回归模型进行了比较。数值结果清楚地表明，在涉及带有或不带有离群值的数据集的情况下，所提出的模型能够提供准确的结果。因此，所提出的模糊回归模型可以成功地应用于提高模糊回归模型在智能系统中的实际应用中的预测准确性和可解释性。