Approximation of Multi-Dimensional Chaotic Dynamics by Using Multi-Stage Fuzzy Inference Systems and the GA

Yoshinori KISHIKAWA  Shozo TOKINAGA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E84-A   No.9   pp.2128-2137
Publication Date: 2001/09/01
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: Chaos & Dynamics
Keyword: 
fuzzy inference,  chaotic dynamics,  multi-stage,  genetic algorithm,  prediction,  

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Summary: 
This paper deals with the approximation of multi-dimensional chaotic dynamics by using the multi-stage fuzzy inference system. The number of rules included in multi-stage fuzzy inference systems is remarkably smaller compared to conventional fuzzy inference systems where the number of rules are proportional 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 method is applied to the approximation of typical multi-dimensional chaotic dynamics. By dividing the inference system into multiple stages, the total number 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 inference rules is optimized by using the GA. Each individual corresponds to an inference system, and its fitness is defined by using the prediction error. Experimental results lead us to a relevant selection of the number of input variables and the number of stages by considering the computational cost and the requirement. Besides the GA in the optimization of membership function, we use the GA to determine the input variables and the number of input. The selection of input variable to each stage, and the number of stages are also discussed. The simulation study for multi-dimensional chaotic dynamics shows that the inference system gives better prediction compared to the prediction by the neural network.