Title :
What is the best shape for a fuzzy set in function approximation?
Author :
Mitaim, Sanya ; Kosko, Bart
Author_Institution :
Signal & Image Process. Inst., Univ. of Southern California, Los Angeles, CA, USA
Abstract :
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
Keywords :
adaptive systems; function approximation; fuzzy set theory; fuzzy systems; learning (artificial intelligence); Gaussian bell curves; adaptive fuzzy system; centroids; function approximation; fuzzy set theory; sinc function; standard additive model; supervised learning; trapezoids; triangles; Explosions; Fires; Function approximation; Fuzzy sets; Fuzzy systems; Measurement standards; Shape; Supervised learning; Tail; Testing;
Conference_Titel :
Fuzzy Systems, 1996., Proceedings of the Fifth IEEE International Conference on
Conference_Location :
New Orleans, LA
Print_ISBN :
0-7803-3645-3
DOI :
10.1109/FUZZY.1996.552354
