×

Transitive calibration of the AHP verbal scale. (English) Zbl 0939.91036

Summary: One of the strengths of the Analytic Hierarchy Process (AHP) is that it allows decision-makers to specify their preferences using a verbal scale. Yet, as is well known, a strict reliance on the corresponding Saaty 1-9 numeric scale can induce some inconsistency. Hence we argue that, in certain situations, it may be appropriate to calibrate the verbal scale. The result of this calibration is a geometric scale based on a single parameter. We present some limited evidence that this geometric scale marginally outperforms the Saaty 1-9 scale. Moreover, we suggest that this calibration can be used to do a simple sensitivity analysis in cases where judgements are uncertain.

MSC:

91B08 Individual preferences
91B06 Decision theory

Keywords:

AHP; scale; calibration
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Arbel, A., Approximate articulation of preference and priority derivation, European journal of operational research, 43, 317-326, (1989) · Zbl 0697.90003
[2] Arbel, A.; Vargas, L.G., Preference simulation and preference programming: robustness issues in priority derivation, European journal of operational research, 69, 200-209, (1993) · Zbl 0783.90002
[3] Barzilai, J.; Cook, W.D.; Golany, B., Consistent weights for judgements matrices of the relative importance of alternatives, Operations research letters, 6, 131-134, (1987) · Zbl 0622.90004
[4] Belton, V.; Gear, T., On a shortcoming of Saaty’s method of analytic hierarchies, Omega, 11, 228-230, (1983)
[5] Dyer, J.S., 1990a. Remarks on the analytic hierarchy process. Management Science 36, 249-258
[6] Dyer, J.S., 1990b. A clarification of ‘Remarks on the analytic hierarchy process’. Management Science 36, 274-275
[7] Harker, P.T.; Vargas, L.G., The theory of ratio scale estimation: Saaty’s analytic hierarchy process, Management science, 33, 1383-1403, (1987)
[8] Harker, P.T., Vargas, L.G., 1990. Reply to ‘Remarks on the Analytic Hierarchy Process’ by J.S. Dyer. Management Science 36, 269-273
[9] Kang, M.; Stam, A., PAHAP: A pairwise aggregated hierarchical analysis of ratio-scale preferences, Decision sciences, 25, 607-624, (1994)
[10] Lootsma, F.A., Scale sensitivity in the multiplicative AHP and SMART, Journal of multi-criteria decision analysis, 2, 87-110, (1993) · Zbl 0838.90009
[11] MacKay, D.B.; Bowen, W.M.; Zinnes, J.L., A Thurstonian view of the analytic hierarchy process, European journal of operational research, 89, 427-444, (1996) · Zbl 0914.90005
[12] Murphy, C.K., Limits on the analytic hierarchy process from its consistency index, European journal of operational research, 67, 138-139, (1993) · Zbl 0775.90009
[13] Paulson, D.; Zahir, S., Consequences of uncertainty in the analytic hierarchy process: A simulation approach, European journal of operational research, 87, 45-56, (1995) · Zbl 0914.90006
[14] Saaty, T.L., A scaling method for priorities in hierarchical structures, Journal of mathematical psychology, 15, 234-281, (1977) · Zbl 0372.62084
[15] Saaty, T.L., 1980. The Analytic Hierarchy Process, McGraw-Hill, New York · Zbl 0587.90002
[16] Saaty, T.L., The analytic hierarchy process: what it is and how it is used, Mathematical modelling, 9, 161-176, (1987) · Zbl 0625.90002
[17] Saaty, T.L., Homogeneity and clustering in the AHP ensures the validity of the scale, European journal of operational research, 72, 598-601, (1994) · Zbl 0800.90009
[18] 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
[19] Schoner, B.; Wedley, W.C., Ambiguous criteria weights in AHP: consequences and solutions, Decision sciences, 20, 462-475, (1989)
[20] Troutt, M.D., Rank reversal and the dependence of priorities on the underlying MAV function, Omega, 16, 365-367, (1988)
[21] Vargas, L.G., Reciprocal matrices with random coefficients, Journal of mathematical modeling, 3, 69-81, (1984) · Zbl 0537.62100
[22] Zahir, M.S., Incorporating the uncertainty of decision judgements in the analytic hierarchy process, European journal of operational research, 53, 206-216, (1991) · Zbl 0729.90589
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.