模糊逻辑中的集合论

Proceedings 31st IEEE International Symposium on Multiple-Valued Logic Pub Date : 2001-05-22 DOI:10.1109/ISMVL.2001.924590

P. Hájek, Z. Haniková

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引用次数: 20

摘要

本文提出了在Hajek的基本模糊逻辑BL风格的模糊逻辑框架内发展公理集理论作为一阶理论的可能性。在经典Zermelo-Fraenkel集合理论中，我们使用了一个布尔值宇宙的构造的类比-在一个特定的真值代数上-我们证明了我们的理论的非平凡性。我们提出了一系列问题和研究任务。

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A set theory within fuzzy 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. 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.

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Proceedings 31st IEEE International Symposium on Multiple-Valued Logic

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