Building a neuro-fuzzy system to efficiently forecast chaotic time series

In this paper we show which elements have to be extracted from a chaotic time series in order to define the architecture of a forecaster. The forecaster chosen here is a Neuro-Fuzzy System (NFS). This NFS is trained by a supervised gradient descent algorithm. The NFS is made of a layer of singleton inputs, a hidden layer of Gaussian membership functions and one output unit. Product is used for rule inference and sum for rule composition. Output is given by a height defuzzifier. Test cases based on Mackey-Glass time series are presented.