What is the best shape for a fuzzy set in function approximation?
Sanya Mitaim, Bart Kosko · Proceedings of IEEE 5th International Fuzzy Systems · 2002
The choice of fuzzy set functions affects how well fuzzy systems approximate functions. The most common fuzzy sets are triangles, trapezoids, and Gaussian bell curves. We compared these sets with many others on a wide range of approximand functions in one, two, and three dimensions. Supervised learning tuned the IF-part set functions and the centroids and volumes of the THEN-part sets. We compared the set functions based on how closely the adaptive fuzzy system converged to the approximand. The sinc function sin(x)/x performed best or nearly best in most cases.