Abstract
A heated discussion has arisen over the “best” priorities derivation method. Using a Monte Carlo simulation this article compares and evaluates the solutions of four AHP ratio scaling methods: the right eigenvalue method, the left eigenvalue method, the geometric mean and the mean of normalized values. Matrices with different dimensions and degree of impurities are randomly constructed. We observe a high level of agreement between the different scaling techniques. The number of ranking contradictions increases with the dimension of the matrix and the inconsistencies. However, these contradictions affect only close priorities.
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Bana e Costa CA, Vansnick J-C (2001) A fundamental criticism to Saaty’s use of the eigenvalue procedure to derive priorities. Working Paper LSEOR 01.42. Retrieved December 2006 from http://www.lse.ac.uk/collections/operationalResearch/research/workingPapers.htm
Barzilai J (1997) Deriving weights from pairwise comparison matrices. J Operat Res Soc (JORS) 48(12):1226–32
Barzilai J (1998) On the decomposition of the value function. Operat Res Lett 22(4–5):159–170
Barzilai J (2001a) Notes on the analytic hierarchy process. In: Proceedings of the NSF Design and Manufacturing Research Conference, pp 1–6
Barzilai J (2001b) Basic principles of measurement. In: Proceedings of the IEEE inter-national conference on syst man cybern pp 395–400
Barzilai J (2002) Notes on measurement and decision theory. In: Proceedings of the NSF design and manufacturing research conference, pp 1–11
Barzilai J, Golany B (1990) Deriving weights from pairwise comparison matrices: the additive case. Operat Rese Lett 9:407–10
Barzilai J, Cook WD, Golany B (1987) Consistent weights for judgements matrices of the relative importance of alternatives. Operat Res Lett 6(1):131–134
Berekoven L, Eckert W, Ellenrieder P (2001) Marktforschung. Methodische Grundlagen und praktische Anwendung, 9. Auflage, Gabler Verlag, Wiesbaden
Blankmeyer E (1987) Approaches to consistency adjustments. J Optim Theory Appl 45:479–488
Brugha C (2000) Relative measurement and the power function. Eur J Operat Res 121(3):627–640
Budescu DV, Zwick R, Rapoport A (1986) A comparison of the eigenvalue method and the geometric mean procedure for ratio scaling. Appl Psychol Meas 10(1):69–78
Chu ATW, Kalabra RE, Spingarn KA (1979) A comparison of two methods for determining the weights of belonging to fuzzy sets. J Optim Theory Appl 27:531–538
Cogger KO, Yu PL (1985) Eigenweight vectors and least distance approximation for revealed preference in pairwise weight ratios. J Optim Theory Appl 46:483–491
Cook WD, Kress M (1988) Deriving weights from pairwise comparison ratio matrices: an axiomatic approach. Eur J Operat Res 37:355–62
Crawford G, Williams C (1985) A note on the analysis of subjective judgement matrices. J Math Psychol 29:387–405
Golany B, Kress M (1993) A multicriteria evaluation of the methods for obtaining weights from ratio-scale matrices. Eur J Operat Res 69:210–202
Golden BL, Wasil EA, Harker PT (1989) The analytic hierarchy process: applications and studies. Springer, Berlin Heidelberg New York
Ishizaka A (2004) The advantages of clusters in AHP. In: The 15th Mini-Euro conference, MUDSM
Ishizaka A, Lusti M (2003) An intelligent tutorial system for AHP. In: The šorić K, Hunjak T, Scitovski R (eds) Proceedings of the 9th international conference on operational research KOI 2002, pp 215–223
Ishizaka A, Lusti M (2004) An expert module to improve the consistency of AHP matrices. Int Trans Operat Res 11(1):97–105
Jensen RE (1984) An alternative scaling method for priorities in hierarchical structures. J Math Psychol 28(3):317–332
Johnson CR, Beine WB, Wang TY (1979) Right-left asymmetry in an eigenvector ranking procedure. J Math Psychol 18:61–64
Harker PT, Vargas L (1987) The theory of ratio scale estimation: saaty’s analytic hierarchy process. Manage Sci 33(11):1383–1403
Lusti M (2002) Data warehousing und data mining, 2nd edn. Springer, Berlin Heidelberg New York
Saaty ThL (1977) A scaling method for priorities in hierarchical structures. J Math Psychol 15:234–281
Saaty ThL (1980) The analytic hierarchy process. Mac Gray-Hill, New York
Saaty ThL (2001a) Decision-making with the AHP: why is the Principal Eigenvector necessary? In: Proceedings of the 6th international symposium on the analytic hierarchy process (ISAHP 2001), pp 383–396
Saaty ThL (2001b) The seven pillars of the analytic hierarchy process. In: Köksalan M et al. (eds) Multiple criteria decision making in the new millennium. In: Proceedings of the 15th conference, MCDM. Lect. Notes Econ. Math. Syst. vol 507, Springer, Berlin Heidelberg New York, pp 15–37
Saaty ThL (2003) Decision-making with the AHP: why is the principal eigenvector necessary?. Eur J Operat Res 145:85–91
Saaty ThL, Vargas LG (1984a) Inconsistency and rank preservation. J Math Psychol 28:205–214
Saaty Th.L., Vargas L.G. (1984b) Comparison of eigenvalue, logarithmic least squares and least squares methods in estimating ratios. Math Model 5:309–324
Salo AA, Hämäläinen RP (1997), On the Measurement of Preferences in the Analytic Hierarchy Process, J Multi-Criteria Decis Anal 6:309–319
Shim JP (1989) Bibliography research on the analytic hierarchy process (AHP). Socio-Econ Plan Sci 23:161–167
Takeda E, Cooger KO, Yu PL (1987) Estimating criterion weights using eigenvectors: a comparative study. Eur J Operat Res 29:360–369
Triantaphyllou E, Pardalos PM, Mann SH (1990) A minimization approach to membership evaluation in fuzzy sets and error analysis. J Optim Theory Appl 66(2):275–287
Vargas LG (1990) An overview of the analytic hierarchy process and its applications. Eur J Operat Res 48(1):2–8
Zahedi F (1986) The analytic hierarchy process: a survey of the method and its applications. Interface 16:96–108
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Ishizaka, A., Lusti, M. How to derive priorities in AHP: a comparative study. cent.eur.j.oper.res. 14, 387–400 (2006). https://doi.org/10.1007/s10100-006-0012-9
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DOI: https://doi.org/10.1007/s10100-006-0012-9