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Remarks about geometric scale in the analytic hierarchy process

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Języki publikacji
EN
Abstrakty
EN
The Analytic Hierarchy Process (AHP) is perhaps the most popular approach to decision-making problems of prioritization. The basis of the AHP is pairwise comparison, which is used to compare alternatives. This comparisons are provided by decision makers usually as linguistic expressions which are next converted to numbers from a fixed set called a scale. The influence of the scale on the quality of prioritization was investigated in a number of papers. One of the most important types of judgment scale is the Geometric Scale. Its elements depend on specific parameters. In this paper, the impact of the choice of this scale’s parameters on errors in priority vectors and on values of the inconsistency indices is studied via Monte Carlo simulations.
Rocznik
Strony
71--82
Opis fizyczny
Bibliogr 25 poz., tab.
Twórcy
  • Institute of Mathematics, Czestochowa University of Technology Czestochowa, Poland
Bibliografia
  • [1] Ishizaka, A., & Labib, A. (2011). Review of the main developments in the analytic hierarchy process. Expert Systems with Applications, 38(11), 14336-14345.
  • [2] Saaty, T.L. (1977). Scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology, 15(3), 234-281.
  • [3] Saaty, T.L. (1980). The Analytic Hierarchy Process. NewYork: McGrawHill.
  • [4] Saaty, T.L. (2008). Decision making with the analytic hierarchy process. International Journal Services Sciences, 1(1), 83-98.
  • [5] Harker, P., & Vargas, L. (1987). The Theory of Ratio Scale Estimation: Saaty’s Analytic Hierarchy Process. Management Science, 33(11), 1383-1403.
  • [6] Lootsma, F. (1989). Conflict resolution via pairwise comparison of concessions. European Journal of Operational Research, 40, 109-116.
  • [7] Salo, A., & Hamalainen, R. (1997). On the measurement of preference in the analytic hierarchy process. Journal of Multi-Criteria Decision Analysis, 6(6), 309-319.
  • [8] Dong, Y., Xu, Y., Li, H., & Dai, M. (2008). A comparative study of the numerical scales and the prioritization methods in AHP. European Journal of Operational Research, 186, 229-242.
  • [9] Dong, Y., Hong, W.-C., Xu, Y., & Yu, S. (2013). Numerical scales generated individually for analytic hierarchy process. European Journal of Operational Research, 229, 654-662.
  • [10] Franek, J., & Kresta, A. (2014). Judgment scales and consistency measure in AHP. Procedia Economics and Finance, 12, 164-173.
  • [11] Starczewski, T. (2017). Remarks on the impact of the adopted scale on the priority estimation quality. Journal of Applied Mathematics and Computational Mechanics, 16(3), 105-116.
  • [12] Zahedi, F. (1986). A simulation study of estimation methods in the analytic hierarchy process. Socio-Economic Planning Sciences, 20, 347-354.
  • [13] Choo, E.U., & Wedley, W.C. (2004). A common framework for deriving preference values from pairwise comparison matrices. Computers and Operations Research, 31, 893-908.
  • [14] Lin, C.-C. (2007). A revised framework for deriving preference values from pairwise comparison matrices. European Journal of Operational Research, 176, 1145-1150.
  • [15] Grzybowski, A.Z. (2012). Note on a new optimization based approach for estimating priority weights and related consistency index. Expert Systems with Applications, 39, 11699-11708.
  • [16] Grzybowski, A.Z. (2016). New results on inconsistency indices and their relationship with the quality of priority vector estimation. Expert Systems with Applications, 43, 197-212.
  • [17] Dijkstra, T.K. (2013). On the extraction of weights from pairwise comparison matrices. Central European Journal of Operations Research, 21, 103-123.
  • [18] Lin, C., Kou, G., & Ergu, D. (2013). An improved statistical approach for consistency test in AHP. Annals of Operations Research, 211(1), 289-299.
  • [19] Starczewski, T. (2016). Relationship between priority ratios disturbances and priority estimation errors. Journal of Applied Mathematics and Computational Mechanics, 15(3), 143-154.
  • [20] Crawford, G., & Williams, C.A. (1985). A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology, 29, 387-405.
  • [21] Koczkodaj,W.W. (1993). A new definition of consistency of pairwise comparisons. Mathematical and Computer Modelling, 18(7), 79-84.
  • [22] Kazibudzki, P.T. (2016). Redefinition of triad’s inconsistency and its impact on the consistency measurement of pairwise comparison matrix. Journal of Applied Mathematics and Computational Mechanics, 15(1), 71-78.
  • [23] Budescu, D.V., Zwick, R., & Rapoport, A. (1986). Comparison of the analytic hierarchy process and the geometric mean procedure for ratio scaling. Applied Psychological Measurement, 10, 69-78.
  • [24] Aguaron, J., & Moreno-Jimenez, J.M. (2003). The geometric consistency index: Approximated thresholds. European Journal of Operational Research, 147, 137-145.
  • [25] Kazibudzki, P.T. (2016). An examination of performance relations among selected consistency measures for simulated pairwise judgments. Annals of Operations Research, 244(2), 525-544.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-42e68530-8b76-4f67-8cb1-900e1aa1aaab
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