×

Ranking by eigenvector versus other methods in the analytic hierarchy process. (English) Zbl 0942.91020

Summary: Counter-examples are given to show that in decision making, different methods of deriving priority vectors may be close for every single pairwise comparison matrix, yet they can lead to different overall rankings. When the judgments are inconsistent, their transitivity affects the final outcome, and must be taken into consideration in the derived vector. It is known that the principal eigenvector captures transitivity uniquely and is the only way to obtain the correct ranking on a ratio scale of the alternatives of a decision. Because of this and of the counter-examples given below, one should only use the eigenvector for ranking in making a decision.

MSC:

91B06 Decision theory
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Saaty, T.L., Fundamentals of decision making and priority theory with the analytic hierarchy process, (1994), RWS Publications Pittsburgh, PA · Zbl 0816.90001
[2] Saaty, T.L., Multicriteria decision making: the analytic hierarchy process, (1988), RWS Publications Pittsburgh PA · Zbl 1176.90315
[3] Barzilai, J.; Cook, W.D.; Golany, B., Consistent weights for judgments matrices of the relative importance of alternatives, Operations research letters, 6, 3, 131-134, (1987) · Zbl 0622.90004
[4] Crawford, G.B., The geometric Mean procedure for estimating the scale of a judgment matrix, Mathl. modelling, 9, 3-5, 327-334, (1987) · Zbl 0624.62108
[5] Saaty, T.L.; Vargas, L.G., Inconsistency and rank preservation, Journal of mathematical psychology, 28, 2, (1984) · Zbl 0557.62093
[6] Saaty, T.L., Eigenvector and logarithmic least squares, European journal of operational research, 48, 156-160, (1990) · Zbl 0707.90003
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.