A set theory within fuzzy logic
20 Citations•2001•
P. Hájek, Z. Haniková
Proceedings 31st IEEE International Symposium on Multiple-Valued Logic
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, and shows the nontriviality of the theory.
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.