AHP判断矩阵权向量的改进最小二乘求解  

Computing Weight Vector of Comparison Matrix in AHP based on Improved Least Square

作　　者：张瑞永[1] 张云[1] 金晓飞[1] 刘宝宏[1] 马宏绪[1] 

机构地区：[1]国防科技大学机电工程与自动化学院,湖南长沙410073

出　　处：《数学的实践与认识》2009年第24期152-157,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(60704038);武器装备预研基金(9140A04030208KG0113)

摘　　要：提出了基于最小二乘法计算判断矩阵权向量的新方法.固定AHP判断矩阵权向量中的一个值为常量,利用判断矩阵的上三角部分元素,设计了一种计算判断矩阵权向量的新算法,算法简单,计算容易,与特征向量排序方法导出标度相同,并且能够证明存在唯一解.实验表明该算法具有有效性和可行性.A new approach based an least square method to calculate the weight vector of comparison matrix in the analytical hierarchy process （AHP） was proposed. Fixing one element of the weight vector as a constant and judging from the upper triangular part of the comparison matrix, this paper designed a new algorithm for calculating the weight vector of comparison matrix, which is simple, easy for computation and of the same derived scale of eigenvector ranking method. The existence and uniqueness of the solution is proved. The experiment indicates that it is valid and practicable.

关 键 词：层次分析法 最小二乘法 权向量 AHP 

分 类 号：O151.21[理学—数学]