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A novel approach for TSK fuzzy modeling with outliers

The TSK type of fuzzy models has attracted a great attention of the fuzzy modeling community due to their good performance in various applications. In the literature, some approaches for modeling TSK fuzzy rules have been proposed. Most of them define their fuzzy subspaces based on the idea of training data being close enough instead of having similar functions. Recently, a new approach, fuzzy c-regression model (FCRM) clustering algorithm, is proposed to construct TSK fuzzy models. However, this approach does not take into account the training data with outliers. In order to overcome the effects of outliers, a robust TSK fuzzy modeling with outliers has been proposed. It is worth noting that this approach may need more computation time due to complicated formulas. Hence, a novel TSK fuzzy modeling approach with outliers is presented in this paper. In this approach, robust fuzzy regression (RFR) clustering algorithm is proposed to simultaneously define fuzzy subspaces and find the parameters in the consequent parts of TSK rules. In the clustering process, the similarity measure is used to reduce the redundant rules. To obtain a more precision model that is not affected by outliers, an annealing robust BP learning algorithm is employed. From the simulation results, the proposed TSK fuzzy model approach indeed showed superior performance.