Barzilai, J.; Cook, W. D.; Golany, B. Consistent weights for judgements matrices on the relative importance of alternatives. (English) Zbl 0622.90004 Oper. Res. Lett. 6, 131-134 (1987). We prove that the only solution satisfying consistency axioms for the problem of retrieving weights from inconcistent judgements matrices whose entries are the relative importance ratios of alternatives is the geometric mean. Cited in 1 ReviewCited in 55 Documents MSC: 91B06 Decision theory Keywords:eigenvector; importance of alternatives; analytic hierarchy process; consistency axioms; retrieving weights; inconcistent judgements matrices; geometric mean PDF BibTeX XML Cite \textit{J. Barzilai} et al., Oper. Res. Lett. 6, 131--134 (1987; Zbl 0622.90004) Full Text: DOI OpenURL References: [1] Birkhoff, G.; MacLane, S., A survey of modern algebra, (1965), Macmillan New York [2] Crawford, G.; Williams, C., A note on the analysis of subjective judgement matrices, J. of mathematical psychology, 29, 387-405, (1985) · Zbl 0585.62183 [3] Johnson, C.R.; Beine, W.B.; Wang, T.J., A note on right-left asymmetry in an eigenvector ranking procedure, J. of mathematical psychology, 19, 61-64, (1979) [4] Saaty, T.L., The analytic hierarchy process, (1980), McGraw-Hill New York · Zbl 1176.90315 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.