On (un)suitable fuzzy relations to model approximate equality (Q1858403)

The authors argue, with reference to some intuitively explained examples, that the standard notion of fuzzy \(T\)-equivalence relation, \(T\) some t-norm, is not a sufficiently convincing formalisation of the (again intuitive) notion of approximate equality, as it is referred to, e.g., in the Poincaré paradox. To solve this problem more suitably they introduce a new class of resemblance relations which are based upon a pseudometric. For such resemblance relations a few properties are proved, and it is argued that they form suitable formalisations of approximate equalities. The papers reviewed below contain a discussion of this attempt.