模糊Domain是Domain理论一个新的分支。本项目将致力于寻找模糊Domain的典型的Cartesian闭子范畴及相关问题的研究。目标是找到模糊Domain的一些典型的Cartesian闭子范畴，并对模糊Domain的Cartesian闭子范畴进行详细分类。从而为模糊Domain在计算机程序设计语言的形式语义学中的应用提供数学基础。主要研究内容包括：（1）模糊Domain映射空间的连续性与模糊Domain的乘积；（2）模糊Domain的拓扑性质及其与映射空间的连续性的关系；（3）模糊Domain关于模糊信息系统的表示，以及如何在模糊信息系统中解Domain方程；（4）寻找模糊Domain的Cartesian闭子范畴，并对其进行分类。

Fuzzy domains are a new branch of Domain theory. This project is devoted to search for Cartesian closed subcategories of fuzzy domains. It aims at discovering several Cartesian closed subcategories of fuzzy domains and classifying the Cartesian closed subcategories of fuzzy domains. This will provide mathematical foundation for the application of fuzzy domains in the study of the semantics of programming languages. The contents of the project include: (1) the continuity of function spaces and the product of fuzzy domains; (2) topological properties of fuzzy domains and their relation to the continuity of function spaces; (3) the representation of fuzzy domains through fuzzy information systems and solving domain equations in fuzzy information systems; (4) searching for Cartesian closed subcategories of fuzzy domains and the classification for them.