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Sugeno controllers with a bounded number of rules are nowhere dense

✍ Scribed by Bernhard Moser

Book ID: 104292548
Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 587 KB
Volume: 104
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(97)00220-0

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✦ Synopsis

In literature various results can be found claiming that fuzzy controllers are universal approximators. In terms of topology this means that fuzzy controllers as subsets of adequate function spaces are dense. In this paper the topological structure of fuzzy controllers composed of a bounded number of rules is investigated. It turns out that these sets are nowhere dense (a topological notion indicating that the sets are "almost discrete"). This means, that it is just the number of rules and, e.g. not the great variety of parameters of fuzzy controllers, why fuzzy controllers are universal approximators.

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