Fuzzy logic and categories of fuzzy sets. (English) Zbl 0827.03039
Höhle, Ulrich (ed.) et al., Non-classical logics and their applications to fuzzy subsets. A handbook of the mathematical foundations of fuzzy set theory. Proceedings of the 14th Linz seminar on fuzzy set theory held at Linz, Austria in the second week of September 1992. Dordrecht: Kluwer Academic Publishers. Theory Decis. Libr., Ser. B. 32, 235-268 (1995).
The paper deals with fuzzy logic, categories of fuzzy sets and logic of fuzzy subsets. A survey of fuzzy logic is presented. Six categories of fuzzy sets, each of them equipped with fuzzy logic, are described and the relationship between them is discussed. For these six categories a generalization of Stout’s theory is given. An appropriate first-order language with interpretations in an underlying category of fuzzy sets is proposed.
For the entire collection see [Zbl 0814.00013].
For the entire collection see [Zbl 0814.00013].
Reviewer: K.Peeva (Sofia)
MSC:
| 03G30 | Categorical logic, topoi |
| 03E72 | Theory of fuzzy sets, etc. |
| 03B52 | Fuzzy logic; logic of vagueness |
