量化Domain理论是把指称语义的Domain理论与度量方法深度结合的一种理论，其本质在于寻找一类能够计算的模型结构，这类模型结构对于研究计算机科学中的并发式语言有着重要的意义。近年来，量化Domain理论发展迅速，但关于模糊有界完备domain范畴的笛卡尔闭性及其Scott拓扑等问题还尚无涉及。对这些内容的研究不仅能进一步拓展量化Domain理论，还能在解决并发式语言的相关问题中起着重要作用。基于此，本项目将借助模糊集和enriched范畴理论，探究量化Domain理论中的笛尔闭范畴及Scott拓扑，拟研究以下四个专题: (1)模糊有界完备domain的理想完备化；(2)模糊有界完备domain范畴的笛卡尔闭性；(3)模糊Scott-domain范畴的笛卡尔闭性；(4)模糊有界完备domain上Scott拓扑的等价刻画。

Quantitative domain theory is regarded as the deep combination of denotational semantics of domain theory and the method of measurement. Its essence is to find a kind of model structure which can be calculated. This kind of model structure has important significance for the research of concurrent language in computer science. In recent years, quantitative domain theory has developed rapidly, but the problems of cartesian closed and Scott topology of fuzzy bounded complete domain categories have not been involved. The study of these contents can not only expand the quantitative domain theory, but also play an important role in solving the related problems of concurrent language. Based on these, this project will use fuzzy set and enriched category theory to explore the properties of cartesian closed categories and Scott topology of quantitative domain theory. The concrete contents of this project include: (1) the ideal completion of fuzzy bounded complete domain. (2) the cartesian closed property of the category of fuzzy bounded complete domain. (3) the cartesian closed property of the category of fuzzy Scott-domain. (4) the equivalent characterization of the Scott topology on fuzzy bounded complete domain.