Approximation of multi-dimensional chaotic dynamics by using multi-stage fuzzy inference systems and the GA

This paper deals with the approximation of multi-dimensional chaotic dynami cs by using the multi-stage fuzzy inference system. The number of rules inc luded in multistage fuzzy inference systems is remarkably smaller compared to conventional fuzzy inference systems where the number of rules are propo rtional to an exponential of the number of input variables. We also propose a method to optimize the shape of membership function and the appropriate selection of input variables based upon the genetic algorithm (GA). The met hod is applied to the approximation of typical multi-dimensional chaotic dy namics. By dividing the inference system into multiple stages, the total nu mber of rules is sufficiently depressed compared to the single stage system . In each stage of inference only a portion of input variables are used as the input, and output of the stage is treated as an input to the next stage . To give better performance, the shape of the membership function of the i nference rules is optimized by using the GA. Each individual corresponds to an inference system, and its fitness is defined by using the prediction er ror. Experimental results lead us to a relevant selection of the number of input variables and the number of stages by considering the computational c ost and the requirement. Besides the GA in the optimization of membership f unction, we use the GA to determine the input variables and the number of i nput. The selection of input variable to each stage, and the number of stag es are also discussed. The simulation study for multi-dimensional chaotic d ynamics shows that the inference system gives better prediction compared to the prediction by the neural network.