×

zbMATH — the first resource for mathematics

Robust estimation of priorities in the AHP. (English) Zbl 1009.90059
Summary: A pairwise comparison matrix of the Analytic Hierarchy Process (AHP) is considered as a contingency table that helps to identify unusual or false data elicited from a judge. Special techniques are suggested for robust estimation of priority vectors. They include transformation of a Saaty matrix to matrix of shares of preferences and solving an eigenproblem designed for the transformed matrices. We also introduce an optimizing objective that produces robust priority estimation. Numerical results are compared using the AHP with these differing approaches. The comparison demonstrates that robust estimations yield priority vectors not prone to influence of possible errors among the elements of a pairwise comparison matrix.

MSC:
90B50 Management decision making, including multiple objectives
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Arbel, A.; Vargas, L.G., The analytic hierarchy process with interval judgements, (), 61-70 · Zbl 0825.90014
[2] Bar Niv (Burnovski), M.; Lipovetsky, S., Deciding circular priorities in insolvency situations, International journal of operations and quantitative management, 1, 183-195, (1995)
[3] Conklin, M., Lipovetsky, S., 1999. Efficient assessment of self-explicated importance using latent class Thurstone scaling. In: The 10th Annual Advanced Research Techniques Forum, American Marketing Association, Santa Fe, New Mexico
[4] Green, P.E.; Tull, D.S., Research for marketing decision, (1978), Prentice-Hall New Jersey
[5] Dodd, F.J.; Donegan, H.A.; McMaster, T.B., Inverse inconsistency in analytic hierarchies, European journal of operational research, 80, 86-93, (1995) · Zbl 0927.91004
[6] Hogg, R.V.; Craig, A.T., Introduction to mathematical statistics, (1969), Macmillan New York · Zbl 0192.25603
[7] Kendall, M.G., Stuart, A., 1974. The Advanced Theory of Statistics, vol. 2. Hafner, London · Zbl 0416.62001
[8] Lipovetsky, S., The synthetic hierarchy method: an optimizing approach to obtaining priorities in the AHP, European journal of operational research, 93, 550-564, (1996) · Zbl 0912.90187
[9] Lipovetsky, S.; Lootsma, F.A., Generalized Golden sections, repeated bisections and aesthetic pleasure, European journal of operational research, 121, 213-216, (2000) · Zbl 0948.91016
[10] Lipovetsky, S.; Tishler, A., Linear methods in multimode data analysis for decision making, Computers and operations research, 21, 169-183, (1994) · Zbl 0797.90052
[11] Lipovetsky, S.; Tishler, A.; Dvir, D.; Shenhar, A., The relative importance of project success dimensions, R&D management, 27, 97-106, (1997)
[12] Lipovetsky, S.; Tishler, A., Interval estimation of priorities in the AHP, European journal of operational research, 114, 153-164, (1999) · Zbl 0938.91016
[13] Lootsma, F., Scale sensitivity in the multiplicative AHP and SMART, Journal of multi-criteria decision analysis, 2, 87-110, (1993) · Zbl 0838.90009
[14] Lootsma, F., Multi-criteria decision analysis via ratio and difference judgement, (1999), Kluwer Academic Publishers Dordrecht · Zbl 0939.91029
[15] Minc, H., Nonnegative matrices, (1988), Willey New York · Zbl 0638.15008
[16] Nakanishi, M., Kinoshita, E., 1996. On the decision maker’s stress in applying Analytic Hierarchy Process. In: Proceedings of the Fourth International Symposium on the Analytic Hierarchy Process. Simon Fraser University, Canada
[17] Paulson, D.; Zahir, M.S., Consequences for uncertainty in the analytic hierarchy process: A simulation approach, European journal of operational research, 87, 45-56, (1995) · Zbl 0914.90006
[18] Salo, A., Inconsistency analysis by approximately specified priorities, Mathematical and computer modelling, 17, 123-133, (1993) · Zbl 0768.90002
[19] Saaty, T.L., The analytic hierarchy process, (1980), McGraw-Hill New York · Zbl 1176.90315
[20] Saaty, T.L., Fundamentals of decision making and priority theory with the analytic hierarchy process, (1994), RWS Publications Pittsburgh, PA · Zbl 0816.90001
[21] Saaty, T.L., Decision making with dependence and feedback: the analytic network process, (1996), RWS Publications Pittsburgh, PA · Zbl 1176.90315
[22] Saaty, T.L.; Kearns, K.P., Analytical planning, (1985), Pergamon Press New York
[23] Saaty, T.L.; Vargas, L.G., Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios, Mathematical modelling, 5, 309-324, (1984) · Zbl 0584.62102
[24] Saaty, T.L.; Vargas, L.G., Uncertainty and rank order in the analytic hierarchy process, European journal of operational research, 32, 107-117, (1987) · Zbl 0632.90002
[25] Saaty, T.L.; Vargas, L.G., Decision making in economic, political, social and technological environment with the analytic hierarchy process, (1994), RWS Publications Pittsburgh, PA
[26] Thurstone, L.L., A law of comparative judgment, Psychological review, 34, 273-286, (1927)
[27] Thurstone, L.L., The measurement of values, (1959), University of Chicago Chicago · Zbl 0063.07377
[28] Tversky, A.; Simonson, I., Context-dependent preferences, Management sciences, 39, 1179-1189, (1993) · Zbl 0800.90037
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.