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.
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机译:基于具有高斯隶属函数的模糊逻辑系统的神经实现,提出了一种神经模糊预测混沌时间序列的方法。为了构建将对混沌时间序列的未来值进行近似和预测的神经模糊系统,将隶属函数的参数(即所选高斯函数的均值(c)和方差(/ spl sigma /))设置为以及模糊区域的中心(y / sup l /)都可以通过反向传播或Levenberg-Marquardt训练算法进行调整。为了检验预测方法的有效性,对性能函数(例如平方和,均方误差和均值绝对误差)进行了评估。以这种方式表明,所提出的神经模糊方法是用于混沌时间序列预测的极好的工具。
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