Abstract: The concepts of weighted α-lower product and weighted α-upper product between a relation matrix and a Boolean column vector are presented in weighted approximation space.The results that weighted α-lower and α-upper products are weighted lower and upper approximations，respectively，are proved，thus a new matrix way to study weighted rough sets（VPRSs，Pawlak rough sets） is given.Finally，an algorithm to computer weighted lower and upper approximations is established.

摘要： 在加权近似空间中提出了关系矩阵和布尔列向量加权α下乘法和加权α上乘法的概念。证明了加权α下乘法就是加权下近似，加权α上乘法就是加权上近似，从而为加权粗糙集（可变精度粗糙集、经典粗糙集）的计算和研究提供了一种新的矩阵方法。最后给出了计算加权上下近似的算法。