×

Negations generated by bounded lattices t-norms. (English) Zbl 1252.03048

Greco, Salvatore (ed.) et al., Advances in computational intelligence. 14th international conference on information processing and management of uncertainty in knowledge-based systems, IPMU 2012, Catania, Italy, July 9–13, 2012. Proceedings, Part III. Berlin: Springer (ISBN 978-3-642-31717-0/pbk; 978-3-642-31718-7/ebook). Communications in Computer and Information Science 299, 326-335 (2012).
Summary: From the birth of fuzzy set theory, several extensions have been proposed changing the possible membership values. Since fuzzy connectives such as t-norms and negations have an important role in theoretical as well as applied fuzzy logics, these connectives have been adapted for these generalized frameworks. Perhaps, an extension of fuzzy logic which generalizes the remaining extensions, proposed by Joseph Goguen in 1967, is to consider arbitrary bounded lattices for the values of the membership degrees. In this paper we extend the usual way of constructing fuzzy negations from t-norms for the bounded lattice t-norms and prove some properties of this construction.
For the entire collection see [Zbl 1251.68017].

MSC:

03B52 Fuzzy logic; logic of vagueness
03E72 Theory of fuzzy sets, etc.
PDFBibTeX XMLCite
Full Text: DOI