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Takagi–Sugeno–Kang (TSK) fuzzy systems have been widely applied for solving function approximation and regression-centric problems. Existing dynamic TSK models proposed in the literature can be broadly classified into two classes. Class I TSK models are essentially fuzzy systems that are limited to time-invariant environments. Class II TSK models are generally evolving systems that can learn in time-variant environments. This paper attempts to address the issues of achieving compact, up-to-date fuzzy rule bases and interpretable knowledge bases in TSK models. It proposes a novel rule pruning method which is simple, computationally efficient and biologically plausible. This rule pruning algorithm applies a gradual forgetting approach and adopts the Hebbian learning mechanism behind the long-term potentiation phenomenon in the brain. It also proposes a merging approach which is used to improve the interpretability of the knowledge bases. This approach can prevent derived fuzzy sets from expanding too many times to protect their semantic meanings. These two approaches are incorporated into a generic self-evolving Takagi–Sugeno–Kang fuzzy framework (GSETSK) which adopts an online data-driven incremental-learning-based approach. Extensive experiments were conducted to evaluate the performance of the proposed GSETSK against other established evolving TSK systems. GSETSK has also been tested on real world dataset using the high-way traffic flow density and Dow Jones index time series. The results are encouraging. GSETSK demonstrates its fast learning ability in time-variant environments. In addition, GSETSK derives an up-to-date and better interpretable fuzzy rule base while maintaining a high level of modeling accuracy at the same time. [ABSTRACT FROM AUTHOR]

In this paper, a new sequential learning algorithm is constructed by combining the Online Sequential Extreme Learning Machine (OS-ELM) and Kalman filter regression. The Kalman Online Sequential Extreme Learning Machine (KOSELM) handles the problem of multicollinearity of the OS-ELM, which can generate poor predictions and unstable models. The KOSELM learns the training data one-by-one or chunk-by-chunk by adjusting the variance of the output weights through the Kalman filter. The performance of the proposed algorithm has been validated on benchmark regression datasets, and the results show that KOSELM can achieve a higher learning accuracy than OS-ELM and its related extensions. A statistical validation for the differences of the accuracy for all algorithms is performed, and the results confirm that KOSELM has better stability than ReOS-ELM, TOSELM and LS-IELM. [ABSTRACT FROM AUTHOR]