Title :
A set theory within fuzzy logic
Author :
Hájek, Petr ; Haniková, Zuzana
Author_Institution :
Inst. of Comput. Sci., Czechoslovak Acad. of Sci., Prague, Czech Republic
Abstract :
This paper proposes a possibility of developing an axiomatic set theory, as first-order theory within the framework of fuzzy logic in the style of Hajek´s Basic fuzzy logic BL. In classical Zermelo-Fraenkel set theory, we use an analogy of the construction of a Boolean-valued universe-over a particular algebra of truth values-we show the nontriviality of our theory. We present a list of problems and research tasks
Keywords :
fuzzy logic; multivalued logic; set theory; Boolean-valued universe; Zermelo-Fraenkel set theory; axiomatic set theory; fuzzy logic; set theory; truth values; Algebra; Computer science; Fuzzy logic; Fuzzy set theory; Inspection; Logic functions; Multivalued logic; Set theory;
Conference_Titel :
Multiple-Valued Logic, 2001. Proceedings. 31st IEEE International Symposium on
Conference_Location :
Warsaw
Print_ISBN :
0-7695-1083-3
DOI :
10.1109/ISMVL.2001.924590
