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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.

In this paper, a stochastic configuration based fuzzy inference system with interpretable fuzzy rules (SCFS-IFRs) is proposed to improve the interpretability and performance of the fuzzy inference system and determine autonomously an appropriate model structure. The proposed SCFS-IFR first accomplishes a fuzzy system through interpretable linguistic fuzzy rules (ILFRs), which endows the system with clear semantic interpretability. Meanwhile, using an incremental learning method based on stochastic configuration, the appropriate architecture of the system is determined by incremental generation of ILFRs under a supervision mechanism. In addition, the particle swarm optimization (PSO) algorithm, an intelligence search technique, is used in the incremental learning process of ILFRs to obtain better random parameters and improve approximation accuracy. The performance of SCFS-IFRs is verified by regression and classification benchmark datasets. Regression experiments show that the proposed SCFS-IFRs perform best on 10 of the 20 data sets, statistically significantly outperforming the other eight state-of-the-art algorithms. Classification experiments show that, compared with the other six fuzzy classifiers, SCFS-IFRs achieve higher classification accuracy and better interpretation with fewer rules.

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