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Zbl 1020.03049
De Cock, Martine; Kerre, Etienne
On (un)suitable fuzzy relations to model approximate equality. (English)
[J] Fuzzy Sets Syst. 133, No.2, 137-153 (2003). ISSN 0165-0114

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. \par To solve this problem more suitably they introduce a new class of resemblance relations which are based upon a pseudometric. \par For such resemblance relations a few properties are proved, and it is argued that they form suitable formalisations of approximate equalities. \par The papers reviewed below contain a discussion of this attempt.
[Siegfried Johannes Gottwald (Leipzig)]

MSC 2000:: *03E72 Fuzzy sets (logic)
68T37 Reasoning under uncertainty
94D05 Fuzzy sets and logic in connection with communication

Keywords: approximate equality; indistinguishability; fuzzy equivalence relations; resemblance relation; Poincaré paradox

Citations: Zbl 1020.03050; Zbl 1020.03051; Zbl 1020.03052; Zbl 1020.03053; Zbl 1020.03054

Cited in: Zbl 1144.03022 Zbl 1059.20064 Zbl 1020.03054 Zbl 1020.03053 Zbl 1020.03052 Zbl 1020.03051 Zbl 1020.03050

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