The paradoxical success of fuzzy logic (Q2740911)

This paper falls into two, only weakly related, parts. The first, slightly mathematical one, proves a particular case of the obvious fact that each logical system has its own notion of logical equivalence: it shows that the addition of the claim of logical equivalence of the propositional formulas \(\neg (A \wedge \neg B)\) and \(B \vee (\neg A \wedge\neg B)\) to fuzzy propositional logic (formulated with \(\wedge,\vee,\neg\) understood as \(\min, \max, 1-\dots\)) forces the collaps of (this) fuzzy logic (in narrow sense) into classical two-valued logic.NEWLINENEWLINENEWLINEThe second part is methodological and intends to discuss principal limitations of fuzzy logic (in the wider sense). But this discussion is, unfortunately, heavily depending on the ``result'' of the first part and thus of very limited importance.NEWLINENEWLINENEWLINEReviewers Remark: This paper is the revised version of a paper presented at the AAAI'93 conference which was honored with a best paper award there. Because of this, the paper raised a lot of controversy (a series of position statements related to this paper are published in the same issue of IEEE Expert, including a reply by Elkan [ibid. 9, 47-49 (1994; Zbl 1009.03533)]).