Fuzzy prediction of chaotic time series based on singular value decomposition

Abstract

For dynamic systems with complex, ill-conditioned, or nonlinear characteristics, the modeling method based on fuzzy sets is very effective to describe the properties of the systems. In this paper, a fuzzy modeling method based on singular value decomposition (SVD) is proposed. First, a fuzzy clustering method is used to confirm the input space of fuzzy model. Then, the recursive least square algorithm with singular value decomposition is applied to estimate the consequent parameters of fuzzy model in order to avoid error delivery and error accumulation. Furthermore, the parameters of fuzzy model are also optimized by the presented algorithm. To demonstrate the performance of this modeling method, simulations on Mackey–Glass time series and Lorenz chaotic system are performed. The results show that this method provides effective and accurate prediction.