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Features of mathematical theories in formal fuzzy logic. (English) Zbl 1202.03034
Melin, Patricia (ed.) et al., Foundations of fuzzy logic and soft computing. 12th International Fuzzy Systems Association world congress, IFSA 2007, Cancun, Mexico, June 18–21, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-72917-4/pbk). Lecture Notes in Computer Science 4529. Lecture Notes in Artificial Intelligence, 523-532 (2007).
Summary: A genuine fuzzy approach to fuzzy mathematics consists in constructing axiomatic theories over suitable systems of formal fuzzy logic. The features of formal fuzzy logics (esp. the invalidity of the law of contraction) entail certain differences in form between theories axiomatized in fuzzy logic and usual theories known from classical mathematics. This paper summarizes the most important differences and presents guidelines for constructing new theories, defining new notions, and proving new theorems in formal fuzzy mathematics.
For the entire collection see [Zbl 1121.03006].

MSC:
03B52 Fuzzy logic; logic of vagueness
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