Fuzzy systems can uniformly approximate continuous functions, but the number of rules increases geometrically with system dimension. Fast simulated annealing that uses alpha stable generating functions to search locally and tunnel through space can solve large optimization problems. Alpha values less than 1 can find the optimal fuzzy rules that approximate a function. The thick tails of these distributions help the annealing algorithm quickly search the solution space. This method can find the fuzzy rules for one and two input fuzzy systems.
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