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To effectively train Takagi-Sugeno-Kang (TSK) fuzzy systems for regressionproblems, a Mini-Batch Gradient Descent with Regularization, DropRule, andAdaBound (MBGD-RDA) algorithm was recently proposed. It has demonstratedsuperior performances; however, there are also some limitations, e.g., it doesnot allow the user to specify the number of rules directly, and only GaussianMFs can be used. This paper proposes two variants of MBGD-RDA to remedy theselimitations, and show that they outperform the original MBGD-RDA and theclassical ANFIS algorithms with the same number of rules. Furthermore, we alsopropose a rule pruning algorithm for TSK fuzzy systems, which can reduce thenumber of rules without significantly sacrificing the regression performance.Experiments showed that the rules obtained from pruning are generally betterthan training them from scratch directly, especially when Gaussian MFs areused.

MBGD-RDA Training and Rule Pruning for Concise TSK Fuzzy Regression Models