HOW TO IMPROVE MAMDANIS APPROACH TO FUZZY CONTROL

Fuzzy control is a methodology that translates ''if''-''then'' rules, A(j1) (x(1)) & ... & A(jn)(x(n)) --> B-j(u), formulated in terms of a natural language, into an actual control strategy u(($) over right arr ow x). Implication of uncertain statements is much more difficult to u nderstand than ''and,'' ''or,'' and ''not.'' So, the fuzzy control met hodologies usually start with translating ''if''-''then'' rules into s tatements that contain only ''and,'' ''not,'' and ''or.'' The first su ch translation was proposed by Mamdani in his pioneer article on fuzzy control. According to this article, a fuzzy control is reasonable iff one of the rules is applicable, i.e., either the first rule is applic able (A(11)(x(1)) & ... & A(1n)(x(n)) & B-1(u)), or the second one is applicable, etc. This approach turned out to be very successful, and i t is still used in the majority of fuzzy control applications. However , as R. Yager noticed, in some cases, this approach is not ideal: Name ly, if for some ($) over right arrow x, we know what u(($) over right arrow x) should be, and add this crisp rule to our rules, then the res ulting fuzzy control for this x may be different from the desired valu e u(($) over right arrow x). To overcome this drawback, Yager proposed to assign priorities to the rules, so that crisp rules get the highes t priority, and use these priorities while translating the rules into a control strategy u(($) over right arrow x). In this article, we show that a natural modification of Mamdani's approach can solve this prob lem without adding any ad hoc priorities. (C) 1995 John Wiley & Sons, Inc.