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Deriving weights from pairwise comparison ratio matrices: An axiomatic approach

1988; Elsevier BV; Volume: 37; Issue: 3 Linguagem: Inglês

10.1016/0377-2217(88)90198-1

1872-6860

Wade D. Cook, Moshe Kress,

Multi-Criteria Decision Making

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.