概念格与粗糙集的关系研究

概念格理论和粗糙集理论是两种不同的知识表示与知识发现的工具，都已被成功应用于许多领域.粗糙集理论的数据表现方式是信息系统，其研究基础是对象之间的等价关系;概念格理论的数据表现方式是形式背景，其研究基础是一种有序的层次结构--概念格.本文讨论了概念格理论与粗糙集理论之间的基本联系;重点分析了形式概念与等价类之间、概念格与分划之间的关系;证明了概念格与分划之间可以相互转换，给出了转换算法，并用例子加以说明.

Study on Relationships between Concept Lattice and Rough Set

Concept lattice theory and rough set theory, two different methods for knowledge representation and knowledge discovery,are successfully applied to many fields. The data studied by concept lattice theory and rough set theory are expressed by information system and formal context respectively. The basis of rough set theory is an equivalence relation on a universe of objects,and that of concept lattice theory is an ordered hierarchical structure - concept lattice. In this paper,the basic connection between concept lattice theory and rough set theory is discussed and relationships between formal concepts and equivalence classes and between concept lattices and partitions are analyzed. It is proved that a concept lattice can be transformed into a partition and vice versa. Meanwhile transformation algorithms and examples are given.