Hybrid Interval Type-2 Mamdani-TSK Fuzzy System for Regression Analysis
Ashish Bhatia, Renato Cordeiro de Amorim, Vito De Feo
TL;DR
The paper tackles the interpretability–accuracy trade-off in fuzzy regression under data uncertainty by introducing HIT2-MTSK, a Hybrid Interval Type-2 Mamdani-TSK fuzzy system. It combines interval Type-2 fuzzification, dual-rule outputs (Mamdani and TSK), and two rule-dominance weights, with Ant Colony Optimization guiding compact rule-base selection and a TSK-weighted mean for defuzzification. Evaluations on six KEEL datasets show state-of-the-art or competitive performance in several cases, with RMSE improvements ranging from $0.4\%$ to $19\%$, and the California Housing case study demonstrates superior RMSE and robust explainability compared with Mamdani FRBS. The results indicate a practical, interpretable, and accurate framework for real-world regression tasks, balancing linguistic transparency with numerical precision.
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%.