Function approximation of nonlinear functions by GA-based fuzzy systems

In this paper, an approach is presented for developing GA-based fuzzy systems to approximate an unknown function with a limited number of input-output data pairs. The basic idea is to first partition the unknown function according to the sorted input data whose corresponding output are the extremes, and the input data is treated as the centers of the fuzzy sets used in the fuzzy system. After the division, each of the small pieces of the unknown function will be a monotonic function. Then, a fuzzy set with easily adjustable slopes is introduced where two adjacent fuzzy sets will form a small piece of the fuzzy system. By adjusting the slopes of the fuzzy sets, each small piece will become a monotonic function. Each small piece of unknown function will be approximated by a corresponding small piece of fuzzy system. Thus, by dividing the unknown function into a number of monotonic functions, it serves as a guideline for using the least requirement of fuzzy sets. Finally, GA technique is used to improve the accuracy of function approximation in each small piece simultaneously. The approach is a proper way to construct the GA-based fuzzy system without incurring any extra information; one example is given to illustrate the simple but powerful method.