Takagi–Sugeno Fuzzy Regression Trees With Application to Complex Industrial Modeling

Fuzzy decision trees (FDTs) is one of the considerably excellent methods. Most of the existing FDTs’ methods are oriented to classification tasks. Applying FDTs to regression tasks may solve complex industrial modeling problems. In this article, we propose the Takagi–Sugeno (T–S) fuzzy regression tree (TSFRT), which uses the hypothesis of “feature screening followed by T–S fuzzy reasoning.” In the TSFRT, the growth process (crisp set theory) can be deemed as feature screening, and each leaf node (fuzzy set theory) is viewed as a T–S inference reasoning system. Thus, the TSFRT becomes a top-down structure. We develop multiple strategies to identify the parameters of the T–S system in the leaf node using sample-by-sample and batch samples. To improve the method's generalization performance, we also generalize an ensemble method with pseudoinverse and ridge regression. The proposed methods are evaluated by several high- and low-dimensional complex industrial processes. The experimental results show that the proposed method remarkably outperforms other popular regression methods.