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On the power of fuzzy logic
Author(s) -
Pacheco Roberto,
Martins Alejandro,
Kandel Abraham
Publication year - 1996
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/(sici)1098-111x(199610)11:10<779::aid-int5>3.0.co;2-w
Subject(s) - fuzzy logic , vagueness , second order logic , mathematics , equivalence (formal languages) , gödel's completeness theorem , discrete mathematics , t norm fuzzy logics , many valued logic , algebra over a field , mathematical economics , computer science , calculus (dental) , fuzzy number , higher order logic , fuzzy set , pure mathematics , artificial intelligence , description logic , medicine , dentistry
In this article we address the issues brought up by Elkan in his article, “The paradoxical success of fuzzy logic,” [ IEEE Expert, 3–8 (1994)]. Elkan's work has caused concern since it purportedly reveals a Fuzzy Logic weakness regarding its theoretical foundations. A further investigation of Elkan's theorem (“Theorem 1”) revealed that its conclusion is not correct. After indicating the points where we disagree with Elkan, we reformulate Theorem 1, calling this new version “Theorem 2.” Theorems 1 and 2 have the same hypotheses but different conclusions. According to Theorem 2 there is a region of points that do hold the equivalence in the hypotheses of Theorem 1. In other words, one does not need to change the definition of logical equivalence in Theorem 1 in order to prove that Fuzzy Logic does not collapse to a two‐valued logic. In a further analysis of Theorem 2 we show that Elkan's work does not affect the power of Fuzzy Logic to model vagueness. © 1996 John Wiley & Sons, Inc.