一种互反判断矩阵残缺值和排序的推断方法及应用  

A Residual Value and Sorting Inference Method for a Reciprocal Judgment Matrix

作　　者：李伟 张明生 陈德强 LI Wei;ZHANG Mingsheng;CHEN Deqiang(College of Data Science and Information Engineering,Guizhou Minzu Universitys,Guiyang 550025,China)

机构地区：[1]贵州民族大学数据科学与信息工程学院,贵阳550025

出　　处：《湖北民族大学学报（自然科学版）》2020年第1期26-31,共6页Journal of Hubei Minzu University:Natural Science Edition

基　　金：贵州省自然科学基金项目(黔科合J字[2014]2092号).

摘　　要：针对多维决策中判断矩阵信息不完整的情况,提出了一种加权最小二乘法拟合残缺值和排序向量的算法.首先,定义了一种残缺矩阵的伴随矩阵表达方式,通过残缺矩阵和其伴随矩阵建立一个非线性最小二乘模型,拟合得到残缺互反判断矩阵的排序向量;然后通过偏差最小化公式解出残缺元素,得到完整的专家判断矩阵,用特征值法求出排序向量;最后,将拟合得到的排序向量和补充完整的判断矩阵排序向量通过几何平均得到最终排序向量.用算例说明了方法的可行性及有效性.Aiming at the incompleteness of the judgment matrix information in multi-dimensional decision making,an algorithm for fitting the residual value and the sorting vector by weighted least squares method is proposed.Firstly,the expression of the adjoint matrix of a defect matrix is defined.A nonlinear least squares model is established by the incomplete matrix and its adjoint matrix,and the sorting vector of the missing reciprocal judgment matrix is fitted.Then the solution is solved by the deviation minimization formula.The missing elements,the complete expert judgment matrix,the eigenvalue method to obtain the sorting vector;finally,the fitted sorting vector and the complementary complete judgment matrix sorting vector are geometrically averaged to obtain the final sorting vector.The feasibility and effectiveness of the method are illustrated by examples.

关 键 词：残缺互反判断矩阵 伴随矩阵 最小二乘法 排序向量 

分 类 号：F830.91[经济管理—金融学] O211.64[理学—概率论与数理统计]