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

2025-10-15

AI Summary

To address the dual challenges of uncertainty modeling and the accuracy–interpretability trade-off in regression tasks, this paper proposes a hybrid regression framework integrating Mamdani and Takagi–Sugeno–Kang (TSK) fuzzy systems. The method introduces a novel hybrid rule structure featuring fuzzy antecedents and crisp consequents, coupled with a dual-dominant-type mechanism that preserves the semantic interpretability of Mamdani rules while substantially improving numerical prediction accuracy. The system incorporates interval type-2 fuzzy logic, Mamdani inference, TSK-style output aggregation, and an end-to-end hybrid training strategy. Extensive experiments on six benchmark datasets demonstrate that the proposed approach achieves top performance on four datasets, outperforms mainstream black-box models on two, and attains overall best results on one. Relative RMSE improvements range from 0.4% to 19%, confirming its effectiveness in jointly optimizing predictive accuracy and model interpretability.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationMultiagent Systems: Multiagent Systems under UncertaintyReasoning under Uncertainty: Relational Probabilistic Models

Application Category

Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingUser Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

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%.

Problem

• Combining Mamdani interpretability with TSK precision for regression
• Handling data uncertainty and ambiguity in predictive modeling
• Improving fuzzy system accuracy while maintaining rule explainability

Innovation

• Hybrid Mamdani-TSK fuzzy system for regression
• Combines interpretability with precision in modeling
• Uses hybrid rules with fuzzy and crisp components