  To effectively train Takagi-Sugeno-Kang (TSK) fuzzy systems for regression
problems, a Mini-Batch Gradient Descent with Regularization, DropRule, and
AdaBound (MBGD-RDA) algorithm was recently proposed. It has demonstrated
superior performances; however, there are also some limitations, e.g., it does
not allow the user to specify the number of rules directly, and only Gaussian
MFs can be used. This paper proposes two variants of MBGD-RDA to remedy these
limitations, and show that they outperform the original MBGD-RDA and the
classical ANFIS algorithms with the same number of rules. Furthermore, we also
propose a rule pruning algorithm for TSK fuzzy systems, which can reduce the
number of rules without significantly sacrificing the regression performance.
Experiments showed that the rules obtained from pruning are generally better
than training them from scratch directly, especially when Gaussian MFs are
used.
