A quality control approach to consistency paradoxes in AHP. (English) Zbl 0938.91015

Summary: The analytic hierarchy process (AHP) requires a specific consistency check of the pairwise comparisons in order to ensure that the decision maker is being neither inconsistent nor random in his or her pairwise comparisons. However, there are many situations where the decision maker has been reasonable, logical and nonrandom in making the pairwise comparison and yet will fail the consistency check. This paper argues against the use of the standard consistency check. If a consistency test is to be done, a quality control approach is recommended.


91B06 Decision theory
Full Text: DOI


[1] Aczel, J.; Saaty, T.L., Procedures for synthesizing ratio judgments, Journal of mathematical psychology, 27, 93-102, (1983) · Zbl 0522.92028
[2] Barzilai, J.; Golany, B., AHP rank reversal, normalization and aggregation rules, Infor, 32, 2, 57-64, (1994) · Zbl 0805.90001
[3] Besterfield, D.H., 1996. Quality Control. Prentice-Hall, Englewood Cliffs, NJ · Zbl 0619.62092
[4] Dadkah, K.M.; Zahedi, F., A mathematical treatment of inconsistency in the analytic hierarchy process, Mathematical computing modelling, 17, 4/5, 111-122, (1993) · Zbl 0768.90001
[5] Grant, E.L., Leavenworth, R.S., 1988. Statistical Quality Control. McGraw-Hill, New York
[6] Hillier, F.S., Xbar and R-chart control limits based on a small number of subgroups, Journal of quality technology, 1, 1, 17-25, (1969)
[7] Lane, E.F.; Verdini, W.A., A consistency test for AHP decision makers, Decision sciences, 20, 575-590, (1989)
[8] Koczkodaj, W.W., A new definition of consistency of pairwise comparisons, Mathematical computing modelling, 18, 7, 79-84, (1993) · Zbl 0804.92029
[9] Monsuur, H., An intrinsic consistency threshold for reciprocal matrices, European journal of operational research, 96, 387-391, (1996) · Zbl 0917.90012
[10] Montgomery, D.C., 1996. Introduction to Statistical Quality Control. Wiley, New York · Zbl 0997.62503
[11] Murphy, C.K., Limits on the analytic hierarchy process from its consistency index, European journal of operational research, 65, 138-139, (1993) · Zbl 0775.90009
[12] Shenkerman, S., Avoiding rank reversal in AHP decision support models, European journal of operational research, 74, 407-419, (1994) · Zbl 0866.90006
[13] Schoner, B.; Wedley, W.; Choo, W.C., A unified approach to AHP with linking pins, European journal of operational research, 64, 384-392, (1993)
[14] Vargas, L.G., A reply to avoiding rank reversal in AHP decision support models, European journal of operational research, 74, 420-425, (1994) · Zbl 0925.90234
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