序是最基本的数学结构之一。利用分明集上的模糊关系，人们已经建立了较为完善的分明集上的模糊序理论。模糊序在模糊集的理论和应用研究中都有十分重要的应用。但是，由于模糊集结构的复杂性，模糊集上模糊序的研究没有取得满意的进展，仍处于起步阶段。本项目旨在利用范畴论方法对模糊集上的序结构进行深入研究，建立系统的模糊集上的序结构理论，并把它应用到模糊集上的模糊拓扑、模糊形式概念分析、模糊粗糙集的研究之中。本项目的完成将深化我们对模糊集的数学结构以及它与其它数学分支之间的内在联系的认识，为模糊集的数学研究的发展做出贡献。

Order is one of the fundamental structures in mathematics.A satisfactory theory of fuzzy orders on crisp sets has already been established making use of fuzzy relations between crisp sets. Fuzzy orders on (crisp) sets have played an important role in applications and theoretic developments of fuzzy sets. But, due to the complexity of fuzzy sets, the investigation of order structures on fuzzy sets is still at the beginning steps. The aim of this project is to establish a theory of orders on fuzzy sets by treating ordered fuzzy sets as categories enriched in a quantaloid, and apply this theory to the study of fuzzy topology, formal concept analysis, rough set theory based on fuzzy sets. The accomplishment of this project will deepen our understanding of the mathematics of fuzzy sets and the intrinsic relationship between fuzzy sets and other mathematical entities, making a contribution to the study of mathematics of fuzzy sets.