Regularized numerical optimization of fuzzy rule bases

This work is devoted to the mathematical analysis and the numerical solution of data-driven optimization for an important class of fuzzy controllers, so-called Sugeno controllers. In contrast to other approaches which optimize the underlying fuzzy sets, we mainly focus on the linear approximation of the output variable according to the input data. While the first approach leads to nonlinear problems, the latter results in a free, linear least squares system to be solved. Therefore this approach can be used for high dimensional problems as well, when due to the increasing complexity nonlinear systems are no longer applicable. By applying Tikhonov regularization we get stable and fast algorithms that create sufficiently optimized controllers; with saving their interpretability. Finally we show, how variable selection can be used to increase interpretability and to reduce computation time.