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Fuzzy systems as universal approximators

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1 Author(s)
Kosko, B. ; Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA

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

Published in:

Computers, IEEE Transactions on  (Volume:43 ,  Issue: 11 )