An adaptive incremental TSK fuzzy system based on stochastic configuration and its approximation capability analysis

The aim of this study is to improve randomized methods for designing a Takagi-Sugeno-Kang (TSK) fuzzy system. A novel adaptive incremental TSK fuzzy system based on stochastic configuration, named stochastic configuration fuzzy system (SCFS), is proposed in this paper. The proposed SCFS determines the appropriate number of fuzzy rules in TSK fuzzy system by incremental learning approach. From the initial system, new fuzzy rules are added incrementally to improve the system performance until the specified performance is achieved. In the process of generation of fuzzy rules, the stochastic configuration supervision mechanism is applied to ensure that the addition of fuzzy rules can continuously improve the performance. The premise parameters of new adding fuzzy rules are randomly assigned adaptively under the supervisory mechanism, and the consequent parameters are evaluated by Moore-Penrose generalized inverse. It has been proved theoretically that the supervisory mechanism can help to ensure the universal approximation of SCFS. The proposed SCFS can reach any predetermined tolerance level when there are enough fuzzy rules, and the training process is finite. A series of synthetic data and benchmark datasets are used to verify SCFS's performance. According to the experimental results, SCFS achieves satisfactory prediction accuracy compared to other models.