Forecasting chaotic time series using neuro-fuzzy approach

A neuro-fuzzy approach for forecasting of chaotic time series is proposed, based on neuro-implementation of a fuzzy logic system with the Gaussian membership functions. To construct the neuro-fuzzy system that will approximate and forecast the future values of a chaotic time series, the parameters of the membership functions, i.e. the mean (c) and the variance (/spl sigma/) of the selected Gaussian functions, as well as the center of fuzzy region (y/sup l/) are to be adjusted either by backpropagation or the Levenberg-Marquardt training algorithm. To examine the effectiveness of the forecasting method the performance function, like the sum squared errors, mean squared errors, and mean absolute errors, are evaluated. In this way it was shown that the proposed neuro-fuzzy approach is an excellent tool for chaotic time series prediction.