METSK-HDe: A multiobjective evolutionary algorithm to learn accurate TSK-fuzzy systems in high-dimensional and large-scale regression problems

Abstract

In this contribution, we propose a two-stage method for Accurate Fuzzy Modeling in High-Dimensional Regression Problems using Approximate Takagi–Sugeno–Kang Fuzzy Rule-Based Systems. In the first stage, an evolutionary data base learning is performed (involving variables, granularities and slight fuzzy partition displacements) together with an inductive rule base learning within the same process. The second stage is a post-processing process to perform a rule selection and a scatter-based tuning of the membership functions for further refinement of the learned solutions. Moreover, the second stage incorporates an efficient Kalman filter to learn the coefficients of the consequent polynomial function in the Takagi–Sugeno–Kang rules. Both stages include mechanisms that significantly improve the accuracy of the model and ensure a fast convergence in high-dimensional and large-scale regression datasets. We tested our approach on 28 real-world datasets with different numbers of variables and instances. Five well-known methods have been executed as references. We compared the different approaches by applying non-parametric statistical tests for pair-wise and multiple comparisons. The results confirm the effectiveness of the proposed method, showing better results in accuracy within a reasonable computing time.