Fuzzy systems as universal approximators

Author

Kosko, Bart

Author_Institution

Dept. of Electr. Eng., Univ. of Southern California, Los Angeles, CA, USA

Volume

43

Issue

11

fYear

1994

fDate

11/1/1994 12:00:00 AM

Firstpage

1329

Lastpage

1333

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;

fLanguage

English

Journal_Title

Computers, IEEE Transactions on

Publisher

ieee

ISSN

0018-9340

Type

jour

DOI

10.1109/12.324566

Filename

324566