粗糙集理论中概念与运算的信息表示*

粗糙集理论对知识进行了形式化定义,为知识处理提供了一套严密的分析工具,但在代数表示下,粗糙集理论的本质不易被理解,并且,尚无高效的知识约简算法.该文首先建立了知识与信息之间的关系;然后,在此基础上给出了粗糙集理论中概念与运算的信息表示;最后,证明了知识约简在信息和代数两种不同表示下是等价的.这些结论有助于人们深刻理解粗糙集理论的本质,同时,为寻找高效的知识约简算法奠定了基础.

An Information Representation of the Concepts and Operations in Rough Set Theory

Rough set theory proposes a formal definition of knowledge and provides a series of tools to deal with knowledge. However, in the algebraic representation of this theory, it is difficult to understand the essence of rough set theory, and efficient algorithm of knowledge reduction has not been found. In this paper, a relationship between knowledge and information is set up, and then based on the relationship an information representation of the concepts and operations about rough set theory is given. Finally, the equivalence properties between information representation and algebraic representation of knowledge reduction are proved. These conclusions are helpful for people to understand the essence of rough set theory and essential to seek new efficient algorithm of knowledge reduction.