On the power of fuzzy logic

In this paper we address lhe issues brought by Elkan in his article, "The Paradoxical Success of Fuzzy Logic" [3]. Elkan's work has caused concem since 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. Afier indicating lhe points where we disagree with Elkan, we reformulate theorem 1, calling this new version "theorem 2". Theorems 1 and 2 have lhe sarna hypotheses but difterent conclusions. Accordil"!g to theorem 2 there is a region of points that do hold lhe equivalence in lhe hypotheses of theorem 1. In olhar words, one does not need to change lhe definition of logical equivalence in theorem 1 in arder 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 aftect lhe power of Fuzzy Logic to model vagueness.