Constructing Concise Instance-Based Takagi–Sugeno–Kang Fuzzy Systems via Multiobjective Particle Swarm Optimization

Takagi-Sugeno-Kang (TSK) fuzzy system has been successfully applied to various practical problems due to its good performance and interpretability. One important prerequisite for the interpretability of a fuzzy system is a concise rule base. However, how to construct a concise TSK fuzzy system more transparently and adaptively from data remains a challenge. In this article, we propose a two-phase framework of constructing concise instance-based TSK fuzzy systems using a novel multi objective particle swarm optimization algorithm with a bimutation strategy (MOPSO-BM). In the first phase, a basic fuzzy system is constructed, where the rule antecedents are initialized based on some representative input instances selected by a sample filtering algorithm, and the consequent parameters are obtained by least squares estimation. Then in the second phase, the proposed MOPSO-BM algorithm is utilized to further reduce the number of fuzzy rules and fine-tune the consequent parameters, resulting in a set of fuzzy systems that achieve a good trade-off between accuracy and interpretability. Users have the flexibility to select the most suitable model based on their specific requirements, or simply via cross validation. Numerical experiments on twelve benchmark datasets have substantiated the superior performance of the proposed framework in designing high-precision and compact TSK fuzzy systems.