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Universal approximation by hierarchical fuzzy systems

✍ Scribed by Li-Xin Wang

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
450 KB
Volume
93
Category
Article
ISSN
0165-0114

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✦ Synopsis

A serious problem limiting the applicability of standard fuzzy controllers is the rule-explosion problem; that is, the number of rules increases exponentially with the number of input variables to the fuzzy controller. A way to deal with this "curse of dimensionality" is to use the hierarchical fuzzy systems. A hierarchical fuzzy system consists of a number of hierarchically connected low-dimensional fuzzy systems. It can be shown that the number of rules in the hierarchical fuzzy system increases linearly with the number of input variables. In this paper, we prove that the hierarchical fuzzy systems are universal approximators; that is, they can approximate any nonlinear function on a compact set to arbitrary accuracy. Our proof is constructive, that is, we first construct a hierarchical fuzzy system in a step-by-step manner, then prove that the constructed fuzzy system satisfies an error bound, and finally show that the error bound can be made arbitrarily small. (~)

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