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Fuzzy Systems as Universal Approximators
November 1994 (vol. 43 no. 11)
pp. 1329-1333

An additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy. An additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input-output state space and averaging patches that overlap. The fuzzy system computes a conditional expectation E|Y|X| if we view the fuzzy sets as random sets. Each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state-space geometry. Neural or statistical clustering systems can approximate the unknown fuzzy patches from training data. These adaptive fuzzy systems approximate a function at two levels. At the local level the neural system approximates and tunes the fuzzy rules. At the global level the rules or patches approximate the function.

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Index Terms:
neural nets; function approximation; curve fitting; fuzzy set theory; universal approximators; additive fuzzy system; fuzzy patches; input-output state space; conditional expectation; commonsense knowledge; state-space geometry; statistical clustering systems; training data; neural system; fuzzy rules.
Citation:
B. Kosko, "Fuzzy Systems as Universal Approximators," IEEE Transactions on Computers, vol. 43, no. 11, pp. 1329-1333, Nov. 1994, doi:10.1109/12.324566
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