Regression Analysis with Type-1 Fuzzy Functions and Feature Selection Methods
TL;DR
Investigating Type-1 Fuzzy Functions combined with several feature selection strategies indicates that integrating feature selection and regularization methods into the T1FF framework provides a promising and flexible approach for regression modelling on complex real-world data.
Abstract
Real-world regression problems often involve noise, redundancy, multicollinearity, and nonlinear relationships that limit the effectiveness of classical models. This study investigates Type-1 Fuzzy Functions (T1FF) combined with several feature selection strategies, with particular emphasis on the integration of Lasso regression into the T1FF framework, which has not been directly examined in prior research. By incorporating Fuzzy C-Means-based membership degrees into the modelling process, T1FF provides a flexible way to capture uncertainty and nonlinear structure without relying on expert-defined fuzzy rules. The proposed framework was evaluated on six datasets, namely Boston, Auto, College, Steel Fatigue Strength, Fish Price, and Smart Pressure Control, using RMSE and MAPE as performance criteria. The results show that T1FF-based models generally outperform classical LM, Ridge, and Lasso models on most datasets, although the best-performing T1FF variant varied depending on dataset characteristics. In particular, the Lasso-based T1FF model yielded competitive results overall and achieved especially strong performance on the College and Fish Price datasets, while Full and Forward T1FF methods showed the most consistent MAPE-based ranking across datasets. Overall, the findings indicate that integrating feature selection and regularization methods into the T1FF framework provides a promising and flexible approach for regression modelling on complex real-world data.