Title :
Fuzzy systems as universal approximators
Author_Institution :
Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA
fDate :
11/1/1994 12:00:00 AM
Abstract :
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
Keywords :
curve fitting; function approximation; fuzzy set theory; neural nets; additive fuzzy system; commonsense knowledge; conditional expectation; fuzzy patches; fuzzy rules; input-output state space; neural system; state-space geometry; statistical clustering systems; training data; universal approximators; Adaptive systems; Costs; Fires; Fuzzy sets; Fuzzy systems; Geometry; Image processing; Signal processing; State-space methods; Training data;
Journal_Title :
Computers, IEEE Transactions on
