Why fuzzy \(\mathcal T\)-equivalence relations do not resolve the Poincaré paradox, and related issues
This is a bunch of (invited) papers which discuss the arguments given by \textit{M. De Cock} and \textit{E. Kerre} [Fuzzy Sets Syst. 133, 137-153 (2003; Zbl 1020.03049)], reviewed above, against the formalisation of the intuitive notion of approximate equality by fuzzy \(T\)-equivalence relations, together with an answer by those authors. On the one hand the authors explain why and to which extent they are not convinced by the arguments of the paper under discussion, e.g. by the vagueness of the notion of approximate equality (Bodenhofer; Zbl 1020.03050) or by the arguments for full reflexivity (Klawonn; Zbl 1020.03053). On the other hand they look at a better understanding of resemblance relations, explaining e.g. that under some additional assumptions resemblances become fuzzy equivalence relations or are very near to such relations (Boixader; Zbl 1020.03051), that they are particular cases of nearness relations (Janiš; Zbl 1020.03052), or that each reflexive and symmetric fuzzy relation is a resemblance (Klawonn). The answer of De Cock and Kerre gives a better explanation of the author's basic ideas related to what they mean by approximate equality, adds some additional and more carefully chosen arguments in favour of the claim they had made in the paper under discussion, and indicates the origins of the notion of resemblance relation in the context of a new modelling of linguistic hedges.
scientific article; zbMATH DE number 1868250