Abstract
A fuzzy system approximates a function by covering the graph of the function with fuzzy rule patches and averaging patches that overlap. But the number of rules grows exponentially with the total number of input and output variables. the best rules cover the extrema or bumps in the function—they patch the bumps. For mean-squared approximation this follows from the mean value theorem of calculus. Optimal rules can help reduce the computational burden. to find them we can find or learn the zeroes of the derivative map and then center input fuzzy sets at these points. Neural systems can then both tune these rules and add rules to improve the function approximation. © 1995 John Wiley & Sons, Inc.
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