On the Functional Equivalence of TSK Fuzzy Systems to Neural Networks, Mixture of Experts, CART, and Stacking Ensemble Regression

Fuzzy systems have achieved great success in numerous applications. However, there are still many challenges in designing an optimal fuzzy system, e.g., how to efficiently train its parameters, how to improve its performance without adding too many parameters, how to balance the trade-off between cooperations and competitions among the rules, how to overcome the curse of dimensionality, etc. Literature has shown that by making appropriate connections between fuzzy systems and other machine learning approaches, good practices from other domains may be used to improve the fuzzy systems, and vice versa. This paper gives an overview on the functional equivalence between Takagi-Sugeno-Kang fuzzy systems and four classic machine learning approaches -- neural networks, mixture of experts, classification and regression trees, and stacking ensemble regression -- for regression problems. We also point out some promising new research directions, inspired by the functional equivalence, that could lead to solutions to the aforementioned problems. To our knowledge, this is so far the most comprehensive overview on the connections between fuzzy systems and other popular machine learning approaches, and hopefully will stimulate more hybridization between different machine learning algorithms.