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How to improve mamdani's approach to fuzzy control

โœ Scribed by Bo Friesen; Vladik Kreinovich


Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
617 KB
Volume
10
Category
Article
ISSN
0884-8173

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โœฆ Synopsis


Fuzzy control is a methodology that translates "if"-"then" rules, Ajl (xI) & . . . & A,,&) + Bj(u), formulated in terms of a natural language, into an actual control strategy u ( x ). Implication of uncertain statements is much more difficult to understand than "and," "or," and "not." So, the fuzzy control methodologies usually start with translating "if"-"then" rules into statements that contain only "and," "not," and "or." The first such translation was proposed by Mamdani in his pioneer article on fuzzy control. According to this article, a fuzzy control is reasonable iff one of the rules is applicable, i.e., either the first rule is applicable (All(xl) & . . . &A,,](x,) &B l ( u ) ) , or the second one is applicable, etc. This approach turned out to be very successful, and it is still used in the majority of fuzzy control applications. However, 5s R. Yager noticed, i n some cases, this approach is not ideal: Namely, if for some x , we know what u ( x ) should be, and add this crisp rule to our rules,Jhen the resulting fuzzy control for this may be different from the desired value u ( x ) . To overcome this drawback, Yager proposed to assign priorities to the rules, so that crisp rules get the highes: priority, and use these priorities while translating the rules into a control strategy u(x). In this article, we show that a natural modification of Mamdani's approach can solve this problem without adding any ad hoc priorities.


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