Chaotic time series prediction based on fuzzy tree

Abstract

In this paper, an adaptive-tree-structure-based fuzzy model is applied to predict chaotic time series. The fuzzy partition of input data set is adaptive to the pattern of data distribution to optimize the number of the subsets automatically by binary-tree model. A fuzzy area around every discriminant edge is set up by the membership functions corresponding to every subset of input data. A complex nonlinear function is obtained by piecewise linear approximation and smoothing the discontinuous at the discriminant edges of subsets to reduce the error of approximation. The fuzzy tree model is evaluated using prediction of the Mackey-Glass, Lorenz and Henon chaotic time series. In comparison with some existing methods, it is shown that the FT is also of less computation and high accuracy.