Chaotic Time Series Prediction by Auto Fuzzy Regression Model

Abstract

Since the pioneering work of Zadeh, fuzzy set theory has been applied to a myriad of areas. Song and Chissom introduced the concept of fuzzy time series and applied some methods to the enrolments of the University of Alabama. Thereafter we apply fuzzy techniques for system identification and apply statistical techniques to modelling system. An automatic methodology framework that combines fuzzy techniques and statistical techniques for nonparametric residual variance estimation is proposed. The methodology framework is creating regression model by using fuzzy techniques. Identification is performed through learning from examples method introduced by Wang and Mendel algorithm. Delta test residual noise estimation is used in order to select the best subset of inputs as well as the number of linguistic labels for the inputs. An experimental result for chaotic time series prediction are compared with statistical model and shows the advantages of the proposed methodology in terms of approximation accuracy, generalization capability and linguistic interpretability.