Generalization Ability of Self-tuning of Fuzzy Rules with different Types of MSFs

Abstract

With the progress of practical applications of the fuzzy theory, it is becoming increasingly difficult to design and tune larger and more complicated systems with the help of fuzzy knowledge alone. Various methods of tuning the fuzzy reasoning rules used for the approximation of given input-output data intended for the solution of such problems have been proposed, including methods combining fuzzy reasoning and neural networks or methods of tuning the fuzzy reasoning rules by using optimization techniques based on genetic algorithms. However, these methods cannot cope with many problems completely, for example, rapid increase of the number of rules and large scale change of fuzzy system as the number of inputs and outputs increases. To overcome these problems, we add a technique of genetic algorithm to the optimization of fuzzy reasoning using the steepest descent method. In a technique of genetic algorithm, this new method can select some kinds of membership functions(MSFs), delete some lengthy rules, and optimize MSFs. In addition, this new method can improve generalization ability as a result of selection of MSFs adapting to the model. The advantages of this new method are proved by numerical examples with multi input and output learning data involving function approximations.