Weakly associative functions on [0, 1] as logical connectives [fuzzy logic]

Author

Kawaguchi, Mayuka F. ; Miyakoshi, Masaaki

Author_Institution

Graduate Sch. of Eng., Hokkaido Univ., Sapporo, Japan

fYear

2004

fDate

19-22 May 2004

Firstpage

44

Lastpage

48

Abstract

This report focuses on a property of conjunctive operators named "weak associativity," which is one of sufficient conditions for the syllogism in fuzzy logic. The authors introduce a class of binary operators on [0, 1], which satisfy the weak associativity and some boundary conditions. Our newly introduced class is broader than the class of t-norms, and is included in that of Galois-operators on [0, 1], which, and of which, the right-residuals form Galois-connections on [0, 1]. In addition, the authors show some methods to construct some weakly associative functions by using the generators of t-norms.

Keywords

Galois fields; fuzzy logic; Galois-connections; Galois-operator right-residuals; conjunctive operators; fuzzy logic syllogism; logical connectives; t-norm generators; weak associativity binary operators; weakly associative functions; Boundary conditions; Concrete; Fuzzy logic; Logic functions; Sufficient conditions; Systems engineering and theory;

fLanguage

English

Publisher

ieee

Conference_Titel

Multiple-Valued Logic, 2004. Proceedings. 34th International Symposium on

ISSN

0195-623X

Print_ISBN

0-7695-2130-4

Type

conf

DOI

10.1109/ISMVL.2004.1319918

Filename

1319918