Mathematical Support for the Geometric Mean when Deriving a Consistent Matrix from a Pairwise Ratio Matrix

article


Choo, E.U.

Wedley, W.C.

Wijnmalen, D.J.D.
A ratio pairwise comparison matrix estimates another matrix of true ratios between objects. From the pairwise comparison matrix, various methods are used to derive a priority vector and associated consistent matrix that also estimates the matrix of true ratios. The distance from the consistent matrix and the true matrix measures the accuracy of a method. The geometric mean is shown to be the only method with error below a basic threshold while being invariant to any reordering and rescaling of columns. Besides being simple to calculate, the geometric mean has excellent performance and many desirable properties.
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pairwise ratio comparisonsRatio scale preferencesrelevant ratio informationGeometryConsistent matricesGeometric meanMatrix measuresPairwise comparison matricespairwise ratio comparisonsPriority vectorRatio scalerelevant ratio informationEstimation
TNO Identifier
954739
Repository link
https://resolver.tno.nl/uuid:f641728b-3519-4520-9c6a-455f825c3270
ISSN
01692968
Source
Fundamenta Informaticae, 144(3-4), pp. 263-278.
Pages
263-278
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