粗集理论的矩阵方法

The Matrix Approaches of Rough Sets

粗糙集理论是近年来发展起来的一种有效的处理不精确、不确定信息的理论,在机器学习及数据挖掘等领域获得了成功的应用,该文用矩阵的方法来研究粗糙集,即从一个二元关系矩阵出发,给出粗糙集上下近似的矩阵描述,实际上是用矩阵的方法重新定义上下近似,矩阵的方法不仅提供了上下近似的简单的计算方法,也提供了一种新的推理的方法,我们还把矩阵方法用于信息系统的约简。

The theory of rough sets deals with the approximation of an arbitrary subset of a universe by two definable or observable subsets called lower and upper approximation.This paper studies some matrix properties of rough sets.The lower and upper approximation operators of rough sets are redefined using the matrix representation.Matrix approach provides an explicit formula for computing lower and upper approximations.The reduction of knowledge using matrix view is researched.The procedure enables us to eliminate all unnecessary knowledge from the knowledge base.