Robust TSK fuzzy modeling for function approximation with outliers

The Takagi–Sugeno–Kang (TSK) type of fuzzy models has attracted a great attention of the fuzzy modeling community due to their good performance in various applications. Various approaches for modeling TSK fuzzy rules have been proposed in the literature. Most of them define their fuzzy subspaces based on the idea of training data being close enough instead of having similar functions. Besides, in real world applications, training data sets often contain outliers. When outliers exist, traditional clustering and learning algorithms based on the principle of least square error minimization may be seriously affects by outliers. Various robust approaches have been proposed to solve this problem in the neural networks and pattern recognition community. In this paper, a novel robust TSK fuzzy modeling approach is presented. In the approach, a clustering algorithm termed as robust fuzzy regression agglomeration (RFRA) is proposed to define fuzzy subspaces in a fuzzy regression manner with robust capability against outliers. To obtain a more precision model, a robust fine-tuning algorithm is then employed. Various examples are used to verify the effectiveness of the proposed approach. From the simulation results, the proposed robust TSK fuzzy modeling indeed showed superior performance over other approaches.