基于特征矩阵的粗糙集关系性质分析与表示定理

Analysis of Relational Properties and Representing Theorems of Rough Set Based on Characteristic Matrix

本文着重研究粗糙集理论基本概念与基本运算的矩阵表示,用特征矩阵描述粗糙集理论中的基本概念,并通过研究特征矩阵运算性质,揭示和刻画粗糙集知识空间的基本代数性质。同时,定义特征矩阵"与积"和"或积"两种逻辑运算,分别对上、下近似概念相对应;针对完备信息系统与不完备信息系统的特点,分析基于对象属性值的相关关系性质,证明不同关系下对象集的上、下近似集和对象关系类的特征矩阵表示定理。

In this paper, the basic notations in the Rough Sets are discussed by using the matrix method. In order to give out a complete matrix description of rough set and its calculations, the both Boolean calculations ＂and-product＂ and ＂or-product＂, corresponding separately to the notations of the up-approximation and the lower-approximation, between the characteristic matrixes are defined. Aim at the characteristics of the complete and non-complete information systems, the associated relational properties are discussed, and the characteristic matrix representing theorems about the up-lower-approximation of rough set and the relational class of the object are proved.