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**Deriving weights from pairwise comparison ratio matrices: An axiomatic approach.**
*(English)*
Zbl 0652.90002

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.

### MSC:

91B06 | Decision theory |

### Keywords:

pairwise comparision ratio matrix; set of axioms; distance measure; weight derivation; goal programming; round robin tournament
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\textit{W. D. Cook} and \textit{M. Kress}, Eur. J. Oper. Res. 37, No. 3, 355--362 (1988; Zbl 0652.90002)

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### References:

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