Improving the Approximation Accuracy of Fuzzy System by an Alternately Optimized LMS Learning of FBF Parameters
Daijin Kim, In-Hyun Cho · Journal of Electrical Engineering and Information Science · 1998
This paper concerns an improvement of the approximation accuracy in the FBF (Fuzzy Basis Function)-based fuzzy system. The improvement is resulted from using the optimal values of input-output model parameters in the series expansions of fuzzy basis functions, where the optimal values are obtained from learning the model parameters by the given training samples. The learning procedure is performed in the alternately manner that the model parameters of IF parts are updated by one LMS (Least Mean Square) method under the fixed THEN part's model parameters and the model parameters of THEN parts are then updated by another LMS method under the fixed IF part's model parameters. These alternative adjustments of model parameters are continued until the mean squared error (MSE) is not reduced any more. We can reduce the MSE further by allowing the FBFs to have different left and right variance values at both sides. The proposed optimized FBF-based fuzzy system is applied to approximate the Mackey-Glass chaotic time-series and the simulation results show that it outperforms the non-trained FBF-based fuzzy system by reducing the MSE to the half approximately.