A Set Theory within Fuzzy Logic

0404315 - UIVT-O 20010099 RIV US eng C - Konferenční příspěvek (zahraniční konf.)
Hájek, Petr - Haniková, Zuzana
A Set Theory within Fuzzy Logic.
Multiple-Valued Logic. Proceedings. Los Alamitos: IEEE Computer Society, 2001, s. 319-323. ISBN 0-7695-1083-3.
[IEEE International Symposium on Multiple-Valued logic /31./. Warsaw (PL), 22.05.2001-24.05.2001]
Grant CEP: GA AV ČR IAA1030004
Výzkumný záměr: AV0Z1030915
Klíčová slova: fuzzy logic * set theory * axiomatic theories
Kód oboru RIV: BA - Obecná matematika

This paper proposes a possibility of developing an axiomatic set theory, as first-order theory within the framework of fuzzy logic in the style Hajek's book. In classical ZFC, we use an analogy of the construction of a Boolean-valued universe - over a particular algebra of truth values - to show the nontriviality of our theory.
Trvalý link: http://hdl.handle.net/11104/0124574