层次分析法正互反矩阵灵敏度的Hadamard乘积分析法

The Analysis Method of Sensitivity of Reciprocal Matrices Based on Hadamard Product

定义了Ⅱ－标准形和Ⅲ－标准形，证明了任一正互反矩阵均可唯一分解为任一种标准形和一个一致性矩阵的Ｈａｄａｍａｒｄ乘积。利用这种分解进行了正互反矩阵的灵敏度分析。结果表明由被扰动矩阵和扰动矩阵的最小偏差法（ＬＤＭ）和对数最小二乘法（ＬＬＳＭ）排序向量可以得到扰动后矩阵在相应方法下的排序向量，而无需计算扰动后矩阵。

In this paper, we define Ⅱ-standard matrices and Ⅲ-standard matrices, show that every reciprocal matrix can be uniquely decomposed into the Hadamard Product of a consistent matrix and any type of standard matrix, which is used to develop a method based on hadamard product of matrices to analyze the sensitivity of reciprocal matrices.