×
Barzilai, Jonathan; Golany, Boaz

Deriving weights from pairwise comparison matrices: The additive case. (English) Zbl 0711.90007

Oper. Res. Lett. 9, No. 6, 407-410 (1990).
Summary: The foundations are laid for an additive version of the Analytic Hierarchy Process by constructing a framework for the study of multiplicative and additive pairwise comparison matrices and the relations between them. In particular, it will be proved that the only solution satisfying consistency axioms for the problem of retrieving weights from inconsistent additive judgements matrices is the arithmetic mean.

Cited in 19 Documents

MSC:

91B06 Decision theory
90B50 Management decision making, including multiple objectives

Keywords:

geometric means; arithmetic mean; Analytic Hierarchy Process; multiplicative and additive pairwise comparison matrices
PDF BibTeX XML Cite
\textit{J. Barzilai} and \textit{B. Golany}, Oper. Res. Lett. 9, No. 6, 407--410 (1990; Zbl 0711.90007)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Barzilai, J.; Cook, W.D.; Golany, B., Consistent weights for judgements matrices of the relative importance of alternatives, Oper. res. lett., 6, 3, 131-134, (1987) · Zbl 0622.90004
[2] Barzilai, J.; Cook, W.D.; Golany, B., The analytic hierarchy process: structure of the problem and its solutions, () · Zbl 0622.90004
[3] Belton, V.; Gear, T., On a shortcoming of Saaty’s method of analytic hierarchies, Omega, 11, 3, 228-230, (1983)
[4] Crawford, G.; Williams, C., A note on the analysis of subjective judgement matrices, J. math. psychology, 29, 387-405, (1985) · Zbl 0585.62183
[5] Dyer, J.S.; Sarin, R.K., Measurable multiattribute value functions, Oper. res., 27, 4, 810-822, (1979) · Zbl 0423.90004
[6] Jensen, R.E., Consistency adjustment surrogacy of human responses in AHP analysis: issues, controversies and state of the art, (), 78284
[7] Kemeny, J.G.; Snell, J.L., Preference ranking: an axiomatic approach, Mathematical models in the social sciences, (1962), Ginn
[8] Krantz, D.H.; Luce, R.D.; Suppes, P.; Teversky, A., ()
[9] Saaty, T.L., The analytic hierarchy process, (1980), McGraw-Hill New York · Zbl 1176.90315
[10] Saaty, T.L., Hierarchies, reciprocal matrices and ratio scales, () · Zbl 0816.90001
[11] Zahedi, F., The analytic hierarchy process — A survey of the method and its applications, Interfaces, 16, 96-108, (1986)
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.