捷克数学家Petr Hajek建立的BL-逻辑（Basic Logic）是模糊逻辑的重要成就，模糊集理论的里程碑。BL-逻辑本质上是基于连续三角模的多值逻辑。本项目探索基于连续三角模的模糊序与模糊拓扑，亦即与BL-逻辑相应的序与拓扑。项目目标是建立以基于连续三角模的模糊序与模糊拓扑的内在联系为核心内容的量化domain理论。研究内容包括基于连续三角模的模糊拓扑、模糊偏序集的模糊Scott拓扑和模糊Scott余拓扑等。本项目的完成将促进模糊逻辑与其它基于模糊集的数学理论的融合，也有助于我们认识多值逻辑在数学实践中的作用。

The BL-logic (Basic Logic) established by the Czech mathematician Petr Hajek is a great success of fuzzy logic, and a milestone in fuzzy set theory. BL-logic is essentially a many-valued logic based on continuous triangular norms. This project explores fuzzy order and fuzzy topology based on continuous triangular norms, i.e., order and topology that correspond to BL-logic. The aim is to establish a theory of quantitative domains that focuses on the interrelationship between order and topology based on continuous triangular norms. The topics include fuzzy topology based on continuous triangular norms, fuzzy Scott topology and fuzzy Scott cotopology of fuzzy partial orders, and etc. This investigation will facilitate the fusion of fuzzy logic and other branches of mathematics based on fuzzy sets, and enhance our understanding of the role of many-valued logic in mathematical practices.