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Some Conflicting Results in the Analytic Hierarchy Process

    https://doi.org/10.1142/S0219622018500517Cited by:13 (Source: Crossref)
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    Abstract

    The analytic hierarchy process (AHP) has been believed to be one of the most pragmatic and widely accepted methods for multi-criteria decision making. However, there have been various criticisms of this method within the last four decades. In this study, the results of AHP contradicting common expectations are examined for both the distributive and ideal modes. Specifically, conflicting priorities, conflicting decisions, and conflicting preference relations are investigated. A decision-making scenario is used throughout the paper and an illustrative example constructed from the decision-making scenario is provided to demonstrate each of the conflicting results recommended by AHP. With a parametric formulation of each unexpected result, the possibility of unexpected results of AHP is generalized irrespective of applying the distributive or ideal mode. The logic and causes of these contradictions are also analyzed. This study shows that AHP is not always reliable, and could lead the decision makers towards incorrect decisions.

    References

    • 1. T. L. Saaty, The Analytic Hierarchy Process, Planning, Priority Setting, Resource Allocation (RWS Publications, PA, USA, 1980). Google Scholar
    • 2. T. L. Saaty, Fundamentals of Decision Making and Priority Theory with the Analytic Hierarchy Process (RWS Publications, PA, USA, 2000). Google Scholar
    • 3. S. H. von Solms, Validity of the AHP/ANP: Comparing apples and oranges, International Journal of the Analytic Hierarchy Process 3(1) (2011) 2–27. Crossref, Google Scholar
    • 4. H. Maleki and S. Zahir, A comprehensive literature review of the rank reversal phenomenon in the analytic hierarchy process, Journal of Multi-criteria Decision Analysis 20(3–4) (2013) 141–155. Crossref, Google Scholar
    • 5. T. L. Saaty, Axiomatic foundation of the analytic hierarchy process, Management Science 32(7) (1986) 841–855. Crossref, Web of Science, Google Scholar
    • 6. S. R. Watson and A. N. S. Freeling, Assessing attribute weights, Omega 10(6) (1982) 582–583. Crossref, Web of Science, Google Scholar
    • 7. V. Belton and A. E. Gear, On a short-coming of Saaty’s method of analytic hierarchies, Omega 11(3) (1983) 228–230. Crossref, Web of Science, Google Scholar
    • 8. J. S. Dyer and H. V. Ravinder, Irrelevant alternatives and the analytic hierarchy process, Working Paper, The University of Texas at Austin (1983). Google Scholar
    • 9. J. S. Dyer, Remarks on the analytic hierarchy process, Management Science 36(3) (1990) 249–258. Crossref, Web of Science, Google Scholar
    • 10. T. L. Saaty, Highlights and critical points in the theory and application of the analytic hierarchy process, European Journal of Operational Research 74(3) (1994) 426–447. Crossref, Web of Science, Google Scholar
    • 11. I. Millet and T. L. Saaty, On the relativity of relative measures — accommodating both rank preservation and rank reversals in the AHP, European Journal of Operational Research 121(1) (2000) 205–212. Crossref, Web of Science, Google Scholar
    • 12. T. L. Saaty, An eigenvalue allocation model for prioritization and planning. Working paper, Energy Management and Policy Center, University of Pennsylvania (1972). Google Scholar
    • 13. T. L. Saaty, A scaling method for priorities in hierarchical structures, Journal of Mathematical Psychology 15(3) (1977) 234–281. Crossref, Web of Science, Google Scholar
    • 14. T. L. Saaty, Rank from comparisons and from ratings in the analytic hierarchy/network processes, European Journal of Operational Research 168(2) (2006) 557–570. Crossref, Web of Science, Google Scholar
    • 15. A. Ishizaka and A. Labib, Review of the main developments in the analytic hierarchy process, Expert Systems with Applications 38(11) (2011) 14336–14345. Web of Science, Google Scholar
    • 16. T. L. Saaty and E. Forman, The Hierarchon: A Dictionary of Hierarchies (Vol. V) (RWS Publications, PA, USA, 1992). Google Scholar
    • 17. C. M. Brugha, Structure of multi-criteria decision-making, Journal of the Operational Research Society 55(11) (2004) 1156–1168. Crossref, Web of Science, Google Scholar
    • 18. G. Kou, D. Ergu, C. Lin and Y. Chen, Pairwise comparison matrix in multiple criteria decision making, Technological and Economic Development of Economy 22(5) (2016) 738–765. Crossref, Web of Science, Google Scholar
    • 19. T. L. Saaty, How to make a decision: The analytic hierarchy process, Interfaces 24(6) (1994) 19–43. Crossref, Web of Science, Google Scholar
    • 20. P. T. Harker and L. G. Vargas, The theory of ratio scale estimation: Saaty’s analytic hierarchy process, Management Science 33(11) (1987) 1383–1403. Crossref, Web of Science, Google Scholar
    • 21. F. A. Lootsma, Conflict resolution via pairwise comparison of concessions, European Journal of Operational Research 40(1) (1989) 109–116. Crossref, Web of Science, Google Scholar
    • 22. E. F. Lane and W. A. Verdini, A consistency test for AHP decision makers, Decision Sciences 20(3) (1989) 575–590. Crossref, Web of Science, Google Scholar
    • 23. E. H. Forman, Random indices for incomplete pairwise comparison matrices, European Journal of Operational Research 48(1) (1990) 153–155. Crossref, Web of Science, Google Scholar
    • 24. D. Ma and X. Zheng, 9/9-9/1 Scale method of AHP, Proc. 2nd Int. Symp. Analytic Hierarchy Process; Vol. I, Pittsburgh, PA (1991), pp. 197–202. Google Scholar
    • 25. H. Donegan, F. Dodd and T. McMaster, A new approach to AHP decision-making, The Statistician 41(3) (1992) 295–302. Crossref, Google Scholar
    • 26. V. Tummala and Y. Wan, On the mean random inconsistency index of the analytic hierarchy process (AHP), Computers and Industrial Engineering 27(S1–4) (1994) 401–404. Crossref, Web of Science, Google Scholar
    • 27. S. A. Webber, B. Apostolou and J. M. Hassell, The sensitivity of the analytic hierarchy process to alternative scale and cue presentations, European Journal of Operational Research 96(2) (1997) 351–362. Crossref, Web of Science, Google Scholar
    • 28. A. A. Salo and R. P. Hämäläinen, On the measurement of preferences in the analytic hierarchy process, Journal of Multi-Criteria Decision Analysis 6(6) (1997) 309–319. Crossref, Google Scholar
    • 29. T. L. Saaty and M. Ozdemir, Negative priorities in the analytic hierarchy process, Mathematical and Computer Modelling 37(9–10) (2003) 1063–1075. Crossref, Web of Science, Google Scholar
    • 30. J. Aguarón and J. M. Moreno-Jiménez, The geometric consistency index: Approximated thresholds, European Journal of Operational Research 147(1) (2003) 137–145. Crossref, Web of Science, Google Scholar
    • 31. J. I. Peláez and M. T. Lamata, A new measure of consistency for positive reciprocal matrices, Computers and Mathematics with Applications 46(12) (2003) 1839–1845. Crossref, Web of Science, Google Scholar
    • 32. P. Ji and R. Jiang, Scale transitivity in the AHP, Journal of the Operational Research Society 54(8) (2003) 896–905. Crossref, Web of Science, Google Scholar
    • 33. I. Millet and B. Schoner, Incorporating negative values into the analytic hierarchy process, Computers and Operations Research 32(12) (2005) 3163–3173. Crossref, Web of Science, Google Scholar
    • 34. J. A. Alonso and M. T. Lamata, Consistency in the analytic hierarchy process: A new approach, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 14(4) (2006) 445–459. Link, Web of Science, Google Scholar
    • 35. N. V. Hovanov, J. W. Kolari and M. V. Sokolov, Deriving weights from general pairwise comparison matrices, Mathematical Social Sciences 55(2) (2008) 205–220. Crossref, Web of Science, Google Scholar
    • 36. T. Kainulainen, P. Leskinen, P. Korhonen, A. Haara and T. Hujala, A statistical approach to assessing interval scale preferences in discrete choice problems, Journal of the Operational Research Society 60(2) (2009) 252–258. Crossref, Web of Science, Google Scholar
    • 37. G. Kou, D. Ergu and J. Shang, Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction, European Journal of Operational Research 236(1) (2014) 261–271. Crossref, Web of Science, Google Scholar
    • 38. W. Pedrycz and M. Song, Analytic hierarchy process (AHP) in group decision making and its optimization with an allocation of information granularity. IEEE Transactions on Fuzzy Systems 19(3) (2011) 527–539. Crossref, Web of Science, Google Scholar
    • 39. W. Pedrycz and F. Gomide, Granular models and human-centric computing, Chapter 14, in Fuzzy Systems Engineering: Toward Human Centric Computing (Wiley-IEEE Press, 2007). Crossref, Google Scholar
    • 40. P. Karczmarek, W. Pedrycz, A. Kiersztyn and P. Rutka, A study in facial features saliency in face recognition: An analytic hierarchy process approach, Soft Computing 21(24) (2017) 7503–7517. Crossref, Web of Science, Google Scholar
    • 41. P. J. M. van Laarhoven and W. Pedrycz, A fuzzy extension of Saaty’s priority theory, Fuzzy Sets and Systems 11(1–3) (1983) 229–241. Crossref, Web of Science, Google Scholar
    • 42. G. Kou and C. Lin, A cosine maximization method for the priority vector derivation in AHP, European Journal of Operational Research 235(1) (2014) 225–232. Crossref, Web of Science, Google Scholar
    • 43. T. Masuda, Hierarchical sensitivity analysis of priority used in analytic hierarchy process, International Journal of Systems Science 21(2) (1990) 415–427. Crossref, Web of Science, Google Scholar
    • 44. R. L. Armacost and J. C. Hosseini, Identification of determinant attributes using the analytic hierarchy process, Journal of the Academy of Marketing Science 22(4) (1994) 383–392. Crossref, Google Scholar
    • 45. E. Triantaphyllou and A. Sánchez, A sensitivity analysis approach for some deterministic multi-criteria decision-making methods, Decision Sciences 28(1) (1997) 151–194. Crossref, Web of Science, Google Scholar
    • 46. Y. F. Huang, Enhancement on sensitivity analysis of priority in analytic hierarchy process, International Journal of General Systems 31(5) (2002) 531–542. Crossref, Web of Science, Google Scholar
    • 47. J. Aguarón and J. M. Moreno-Jiménez, Local stability intervals in the analytic hierarchy process, European Journal of Operational Research 125(1) (2000) 113–132. Crossref, Web of Science, Google Scholar
    • 48. H. Chen and D. F. Kocaoglu, A sensitivity analysis algorithm for hierarchical decision models, European Journal of Operational Research 185(1) (2008) 266–288. Crossref, Web of Science, Google Scholar
    • 49. G. Kou, Y. Peng and G. Wang, Evaluation of clustering algorithms for financial risk analysis using MCDM methods, Information Sciences 27 (2014) 1–12. Crossref, Web of Science, Google Scholar
    • 50. G. Kou, Y. Lu, Y. Peng and Y. Shi, Evaluation of classification algorithms using MCDM and rank correlation, International Journal of Information Technology & Decision Making 11(1) (2012) 197–225. Link, Web of Science, Google Scholar
    • 51. J. S. Dyer, A clarification of Remarks on the analytic hierarchy process, Management Science 36(3) (1990) 274–275. Crossref, Web of Science, Google Scholar
    • 52. P. Leskinen, Measurement scales and scale independence in the analytic hierarchy process, Journal of Multi-Criteria Decision Analysis 9(4) (2000) 163–174. Crossref, Google Scholar
    • 53. R. D. Holder, Some comments on the analytic hierarchy process, Journal of the Operational Research Society 41(11) (1990) 1073–1076. Crossref, Web of Science, Google Scholar
    • 54. R. C. van den Honert and F. A. Lootsma, Group preference aggregation in the multiplicative AHP: The model of the group decision process and Pareto optimality, European Journal of Operational Research 96(2) (1996) 363–370. Crossref, Web of Science, Google Scholar
    • 55. J. Barzilai, On MAUT, AHP and PFM, Proc. 5th Int. Symp. Analytic Hierarchy Process ( Kobe, Japan, August 1999), pp. 57–60. Google Scholar
    • 56. C. A. Bana e Costa and J.-L. Vansnick, A critical analysis of the eigenvalue method used to derive priorities in AHP, European Journal of Operational Research 187(3) (2008) 1422–1428. Crossref, Web of Science, Google Scholar
    • 57. J. Barzilai and B. Golany, AHP rank reversal, normalization and aggregation rules, INFOR: Information Systems and Operational Research 32(2) (1994) 57–63. Crossref, Google Scholar
    • 58. J. Pérez, Some comments on Saaty’s AHP, Management Science 41(6) (1995) 1091–1095. Crossref, Web of Science, Google Scholar
    • 59. J. S. Finan and W. J. Hurley, The analytic hierarchy process: Can wash criteria be ignored? Computers and Operations Research 29(8) (2002) 1025–1030. Crossref, Web of Science, Google Scholar
    • 60. J. Pérez, J. L. Jimeno and E. Mokotoff, Another potential strong shortcoming of AHP, TOP: Journal of the Spanish Society of Statistics and Operations Research 14(1) (2006) 99–111. Google Scholar
    • 61. A. Ishizaka and A. Labib, Analytic hierarchy process and expert choice: Benefits and limitations, OR Insight 22(4) (2009) 201–220. Crossref, Google Scholar
    • 62. T. L. Saaty and L. G. Vargas, The analytic hierarchy process: Wash criteria should not be ignored, International Journal of Management and Decision Making 7(2–3) (2006) 180–188. Crossref, Google Scholar
    • 63. T. L. Saaty, L. G. Vargas and R. Whitaker, Addressing with brevity criticisms of the analytic hierarchy process. International Journal of the Analytic Hierarchy Process 1(2) (2009) 121–134. Crossref, Google Scholar
    • 64. T. L. Saaty, Response to holder’s comments on the analytic hierarchy process, Journal of the Operational Research Society 42(10) (1991) 909–914. Crossref, Web of Science, Google Scholar
    • 65. R. Whitaker, Why Barzilai’s criticisms of the AHP are incorrect, International Meeting of the Multi-Criteria Decision Making Society, Whistler, Canada (2004). Google Scholar
    • 66. R. Whitaker, Criticisms of the analytic hierarchy process: Why they often make no sense, Mathematical and Computer Modeling 46(7–8) (2007) 948–961. Crossref, Web of Science, Google Scholar
    • 67. R. Whitaker, Validation examples of the analytic hierarchy process and analytic network process, Mathematical and Computer Modeling 46(7–8) (2007) 840–859. Crossref, Web of Science, Google Scholar
    • 68. T. Tyszka, Contextual multi attribute decision rules, in Human Decision Making, eds. L. Sjoberg, T. Tyszka and J. A. Wise (Doxa, Bodafors, Sweden, 1983), pp. 243–256. Google Scholar
    • 69. T. L. Saaty and L. G. Vargas, The legitimacy of rank reversal, Omega 12(5) (1984) 513–516. Crossref, Web of Science, Google Scholar
    • 70. P. T. Harker and L. G. Vargas, Reply to Remarks on the analytic hierarchy process by J. S. Dyer, Management Science 36(3) (1990) 269–273. Crossref, Web of Science, Google Scholar
    • 71. T. L. Saaty, An exposition of the AHP in reply to the paper: Remarks on the analytic hierarchy process, Management Science 36(3) (1990) 259–268. Crossref, Web of Science, Google Scholar
    • 72. T. L. Saaty, Rank and the controversy about the axioms of utility theory— A comparison of AHP and MAUT, 2nd Int. Symp. Analytic Hierarchy Process, Pittsburgh, PA, USA (1991), pp. 87–111. Google Scholar
    • 73. E. H. Forman, Multicriteria prioritization in open and closed systems, Working paper, George Washington University (1992). Google Scholar
    • 74. P. H. Farquhar and A. R. Pratkanis, Decision structuring with phantom alternatives, Management Science 39(10) (1993) 1214–1226. Crossref, Web of Science, Google Scholar
    • 75. A. Tversky, P. Slovic and D. Kahneman, The causes of preference reversal, The American Economic Review 80(1) (1990) 204–217. Web of Science, Google Scholar
    • 76. A. Tversky and I. Simonson, Context-dependent preferences, Management Science 39(10) (1993) 1179–1189. Crossref, Web of Science, Google Scholar
    • 77. T. L. Saaty and L. G. Vargas, Experiments on rank preservation and reversal in relative measurement, Mathematical and Computer Modeling 17(4–5) (1993) 13–18. Crossref, Web of Science, Google Scholar
    • 78. J. Barzilai, W. D. Cook and B. Golany, Consistent weights for judgment matrices of the relative importance of alternatives, Operations Research Letters 6(3) (1987) 131–134. Crossref, Web of Science, Google Scholar
    • 79. B. Schoner and W. C. Wedley, Ambiguous criteria weights in AHP: Consequences and solutions, Decision Sciences 20(3) (1989) 462–475. Crossref, Web of Science, Google Scholar
    • 80. F. A. Lootsma, Numerical scaling of human judgment in pariwise-comparison methods for fuzzy multi-criteria decision analysis, in Mathematical Models for Decision Support, eds. G. Mitra, H. J. Greenberg, F. A. Lootsma, M. J. Rijckaert and H. J. Zimmermann (Springer-Verlag, Berlin, 1988), pp. 57–88. Crossref, Google Scholar
    • 81. F. A. Lootsma, Scale sensitivity in the multiplicative AHP and SMART, Journal of Multi-Criteria Decision Analysis 2(2) (1993) 87–110. Crossref, Google Scholar
    • 82. B. Schoner, W. C. Wedley and E. U. Choo, A unified approach to AHP with linking pins, European Journal of Operational Research 64(3) (1993) 384–392. Crossref, Web of Science, Google Scholar
    • 83. L. G. Vargas, Reply to Schenkerman’s avoiding rank reversal in AHP decision support models, European Journal of Operational Research 74(3) (1994) 420–425. Crossref, Web of Science, Google Scholar
    • 84. J. Barzilai and F. A. Lootsma, Power relations and group aggregation in the multiplicative AHP and SMART, Journal of Multi-Criteria Decision Analysis 6(3) (1997) 155–165. Crossref, Google Scholar
    • 85. B. Schoner, E. U. Choo and W. C. Wedley, A comment on ‘Rank disagreement: A comparison of multicriteria methodologies’, Journal of Multi-Criteria Decision Analysis 6(4) (1997) 197–200. Crossref, Google Scholar
    • 86. L. G. Vargas, Comments on Barzilai and Lootsma: Why the multiplicative AHP is invalid: A practical counter example, Journal of Multi-Criteria Decision Analysis 6(3) (1997) 169–170. Crossref, Google Scholar
    • 87. J. Barzilai, Deriving weights from pairwise comparison matrices, Journal of the Operational Research Society 48(12) (1997) 1226–1232. Crossref, Web of Science, Google Scholar
    • 88. A. Stam and A. P. D. Silva, Stochastic judgments in the AHP: The measurement of rank reversal probabilities, Decision Sciences 28(3) (1997) 655–688. Crossref, Web of Science, Google Scholar
    • 89. A. Stam and A. P. D. Silva, On multiplicative priority rating methods for the AHP, European Journal of Operational Research 145(1) (2003) 92–108. Crossref, Web of Science, Google Scholar
    • 90. S. Zahir, Normalisation and rank reversals in the additive analytic hierarchy process: A new analysis, International Journal of Operational Research 4(4) (2009) 446–467. Crossref, Google Scholar
    • 91. W. Wu and G. Kou, A group consensus model for evaluating real estate investment alternatives, Financial Innovation 2(8) (2016) 3–10. Google Scholar