DERIVING WEIGHTS FROM PAIRWISE COMPARISON RATIO MATRICES - AN AXIOMATIC APPROACH

被引：72

作者：

COOK, WD ^{[1
]}

KRESS, M ^{[1
]}

机构：

[1] CEMA,HAIFA,ISRAEL

来源：

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH | 1988年 / 37卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Axiomatic Approach - Distance Function Uniqueness - Minimum Distance Transitive Matrix - Pairwise Comparison Ratio Matrices;

D O I：

10.1016/0377-2217(88)90198-1

中图分类号：

C93 [管理学];

学科分类号：

12 ; 1201 ; 1202 ; 120202 ;

摘要：

The paper examines the problem of extracting object or attribute weights from a pairwise comparison ratio matrix. This problem is approached from the point of view of a distance measure on the space of all such matrices. A set of axioms is presented which such a distance measure should satisfy, and the uniqueness of the measure is proven. The problem of weight derivation is then shown to be equivalent to that of finding a totally transitive matrix which is a minimum distance from the given matrix. This problem reduces to a goal programming model. Finally, it is shown that the problem of weight derivation is related to that of ranking players in a round robin tournament. The space of all binary tournament matrices is proven to be isometric to a subset of the space of ratio matrices.

引用

页码：355 / 362

页数：8

共 16 条

[1] ON THE MINIMUM VIOLATIONS RANKING OF A TOURNAMENT [J].