arXiv:2510.13437cs.LG2025-10

融合模糊与精确推理,提升回归模型的准确性和可解释性。

Hybrid Interval Type-2 Mamdani-TSK Fuzzy System for Regression Analysis

  • 设计混合规则结构,结合模糊与清晰成分及双主导类型。
  • 在6个数据集上4次超越现有模糊方法,1次整体最优,误差降低0.4%至19%。
  • 适合需要高可解释性又不失精度的金融、医疗等场景建模。

回归分析用于研究输入变量与连续输出变量间的关系,广泛应用于金融、医疗和工程等领域的预测建模。然而,传统方法难以应对现实数据中的不确定性与模糊性。深度学习虽能捕捉复杂非线性关系,但缺乏可解释性且易在小样本上过拟合。模糊系统提供了处理不确定性的替代框架,Mamdani系统强调可解释性,TSK系统追求精度。本文提出一种新型模糊回归方法,融合Mamdani系统的可解释性与TSK模型的精准性。该方法引入含模糊与清晰成分的混合规则结构及双主导类型,兼顾准确率与可解释性。在6个基准数据集上的评估显示,该方法在4个数据集上取得最佳模糊方法表现,在2个数据集上优于黑箱模型,并在1个数据集上获得最佳综合评分,均方根误差(RMSE)改进幅度为0.4%至19%。

原文摘要 · Abstract (English)

Regression analysis is employed to examine and quantify the relationships between input variables and a dependent and continuous output variable. It is widely used for predictive modelling in fields such as finance, healthcare, and engineering. However, traditional methods often struggle with real-world data complexities, including uncertainty and ambiguity. While deep learning approaches excel at capturing complex non-linear relationships, they lack interpretability and risk over-fitting on small datasets. Fuzzy systems provide an alternative framework for handling uncertainty and imprecision, with Mamdani and Takagi-Sugeno-Kang (TSK) systems offering complementary strengths: interpretability versus accuracy. This paper presents a novel fuzzy regression method that combines the interpretability of Mamdani systems with the precision of TSK models. The proposed approach introduces a hybrid rule structure with fuzzy and crisp components and dual dominance types, enhancing both accuracy and explainability. Evaluations on benchmark datasets demonstrate state-of-the-art performance in several cases, with rules maintaining a component similar to traditional Mamdani systems while improving precision through improved rule outputs. This hybrid methodology offers a balanced and versatile tool for predictive modelling, addressing the trade-off between interpretability and accuracy inherent in fuzzy systems. In the 6 datasets tested, the proposed approach gave the best fuzzy methodology score in 4 datasets, out-performed the opaque models in 2 datasets and produced the best overall score in 1 dataset with the improvements in RMSE ranging from 0.4% to 19%.

模糊系统回归分析可解释性模型融合

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