Article ID: | iaor1988690 |
Country: | Netherlands |
Volume: | 37 |
Issue: | 3 |
Start Page Number: | 355 |
End Page Number: | 362 |
Publication Date: | Dec 1988 |
Journal: | European Journal of Operational Research |
Authors: | Cook Wade D., Kress Moshe |
This 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.