Deriving weights from pairwise comparison ratio matrices: An axiomatic approach
type: Item
instance of: scholarly article
title: Deriving weights from pairwise comparison ratio matrices: An axiomatic approach
zbMATH Open document ID: 0652.90002
DOI: 10.1016/0377-2217(88)90198-1
author: Wade D. Cook
author: Moshe Kress
published in: European Journal of Operational Research
publication date: 1988-01-01T00:00:00Z
review text: This paper examines the problem of extracting object or attribute weights from a pairwise comparision 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.
Mathematics Subject Classification ID: 91B06
zbMATH DE Number: 4064696
zbMATH Keywords: pairwise comparision ratio matrix
zbMATH Keywords: set of axioms
zbMATH Keywords: distance measure
zbMATH Keywords: weight derivation
zbMATH Keywords: goal programming
zbMATH Keywords: round robin tournament
MaRDI profile type: Publication
full work available at URL: 0377-2217(88)90198-1
OpenAlex ID: W1967778360
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description: scientific article; zbMATH DE number 4064696