粗糙集理论研究的矩阵方法

Matrix approach to the study of rough set theory

针对粗糙集研究中集合之间关系的计算问题,提出了一种基于矩阵的度量和计算方法。该方法通过引入类矩阵算子、关系矩阵算子、集合矩阵等概念和借助水平截矩阵,得到集合的矩阵表示以及集合与等价类之间关系的矩阵计算。通过对该方法的一些基本性质讨论,给出了该方法在变精度粗糙集模型中属性约简的具体步骤,并用实例说明了其有效性。

Aiming at the computational problem of rough sets, a measure and computational approoen to studying rough set theory based on matrixes is proposed. The approach acquires a measure set denoted in the form of matrixes and the matrix computation of relationships between set and equivalent class by introducing some basic concepts such as class matrix operator, relation matrix operator, set matrix, and with the help of the level cut matrix of product matrixes. The properties of the method are also disscussed. The steps of attributes reduction about the approach applied to a variable precision rough set model are presented. The correctness and effectiveness of the new approach are shown with an example.