whv the Success of Fuzzy Logic is not??aradoxical
نویسنده
چکیده
Elkan’s paper consists of two almost unrelated parts. In the first section, Elkan arrives at the conclusion that an apparently reasonable version of fuzzy logic collapses mathematically to two-valued logic. In the second section, he questions the value of fuzzy logic in control applications and concludes that fuzzy logic does not provide an effective tool for dealing with the problem of uncertainty in knowledge-based systems. As I see it, the first conclusion is based on faulty reasoning, while the second reflects a misconception of what fuzzy logic is and a misunderstanding of the role it plays in control and knowledgebased systems applications. It is easy to show why Elkan’s mathematical analysis is faulty. What he really shows is that fuzzy logic is not consistent with the law of the excluded middle. This, of course, applies in general to multivalued logical systems. The law of the excluded middle asserts that the truth value of any logical expression of the form B v 4 is T (true). The law of contradiction asserts that the truth value of any logical expression of the form B A 4 is F (false). Immediate consequences of these laws in two-valued propositional calculus are as follows:
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