The design of multi-stage fuzzy inference systems with smaller number of rules based upon the optimization of rules by using the GA

This paper shows the design of multi-stage fuzzy inference system with smal ler number of rules based upon the optimization of rules by using the genet ic algorithm. Since the number of rules of fuzzy inference system increases exponentially in proportion to the number of input variables powered by th e number of membership function, it is preferred to divide the inference sy stem into several stages (multi-stage fuzzy inference system) and decrease the number of rules compared to the single stage system. In each stage of i nference only a portion of input variables are used as the input, and the o utput 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 weig ht 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 fun ction is represented as a set of string to which the crossover and mutation operation is applied. By combining the backpropagation algorithm and the G A, we have a comprehensive optimization scheme of learning for the multi-st age fuzzy inference system. The inference system is applied to the automati c bond rating based upon the financial ratios obtained from the financial s tatement by using the prescribed evaluation of rating published by the rati ng 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.