The Design of Multi-Stage Fuzzy Inference Systems with Smaller Number of Rules Based upon the Optimization of Rules by Using the GA

Kangrong TAN  Shozo TOKINAGA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.9   pp.1865-1873
Publication Date: 1999/09/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and Its Applications)
Category: 
Keyword: 
multi-stage inference,  membership function,  genetic algorithm,  backpropagation,  bond rating,  

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Summary: 
This paper shows the design of multi-stage fuzzy inference system with smaller number of rules based upon the optimization of rules by using the genetic algorithm. Since the number of rules of fuzzy inference system increases exponentially in proportion to the number of input variables powered by the number of membership function, it is preferred to divide the inference system into several stages (multi-stage fuzzy inference system) and decrease the number of rules compared to the single stage system. In each stage of inference only a portion of input variables are used as the input, and the output of the stage is treated as an input to the next stage. If we use the simplified inference scheme and assume the shape of membership function is given, the same backpropagation algorithm is available to optimize the weight of each rule as is usually used in the single stage inference system. On the other hand, the shape of the membership function is optimized by using the GA (genetic algorithm) where the characteristics of the membership function is represented as a set of string to which the crossover and mutation operation is applied. By combining the backpropagation algorithm and the GA, we have a comprehensive optimization scheme of learning for the multi-stage fuzzy inference system. The inference system is applied to the automatic bond rating based upon the financial ratios obtained from the financial statement by using the prescribed evaluation of rating published by the rating institution. As a result, we have similar performance of the multi-stage fuzzy inference system as the single stage system with remarkably smaller number of rules.