A fuzzy logic based method for chaotic time series prediction

In this paper, a fuzzy logic based method for single or multi-dimensional Chaotic Time Series (CTS, hereafter) predictions is proposed. The fundament characteristic of CTS is that it demonstrates both stochastic behavior in time domain and determined behavior in phase space. The motivation of this research is two folds: (1) embedding phase space track of CTS data has proven to be a quantitative analysis of a dynamic system in different embedding dimensions; (2) Fuzzy Logic (FL) not only has capability of handling a much more complex systems, but its superiority in time convergence has also proven to be a valuable asset for time critical applications. The process of using the proposed method for CTS predictions includes the following steps: (1) reconstructing a phase space using CTS; (2) using known phase space points to construct the input-output pairs; (3) using a fuzzy system to predict the unknown embedding phase space points; (4) predicting the CTS data by converting the phase space points to the time domain. A C++ program is written to simulate the process. The simulation results show that the proposed method is simple, practical and effective.