A set theory within fuzzy logic

摘要

This paper proposes a possibility of developing an axiomatic settheory, as first-order theory within the framework of fuzzy logic in thestyle of Hajek's Basic fuzzy logic BL. In classical Zermelo-Fraenkel settheory, we use an analogy of the construction of a Boolean-valueduniverse-over a particular algebra of truth values-we show thenontriviality of our theory. We present a list of problems and researchtasks