The Rank Reversals Paradox in Management Decisions: The Comparison of the AHP and COMET Methods

  • Wojciech SałabunEmail author
  • Paweł Ziemba
  • Jarosław Wątróbski
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 56)


Making decisions include many areas of human activity, as well as the management of the organization. Actually, decision-making requires a consideration of rapidly changing options from multiple sources. For this reason, the decision-making process requires modification, which allows processing of a set of alternatives on the fly. The most popular method in this field is the AHP method. However, a serious shortcoming is known, which does not allow to reliably carry out this process. This problem is known as the RankReversals phenomenon. The paper identifies the problem and highlights the importance in the context of numerical examples. These examples are also solved by using the COMET method, which uses a pairwise comparison also. The COMET method is completely free of rank reversal paradox and can be used in exchange for the AHP method.


Rank reversal AHP MCDA COMET Fuzzy logic 


  1. 1.
    Wątróbski, J., Jankowski, J.: Knowledge management in MCDA domain. In: 2015 Federated Conference on Computer Science and Information Systems (FedCSIS), pp. 1445–1450. IEEE (2015)Google Scholar
  2. 2.
    Wątróbski, J., Ziemba, P., Wolski, W.: Methodological aspects of decision support system for the location of renewable energy sources. In: 2015 Federated Conference on Computer Science and Information Systems (FedCSIS), pp. 1451–1459. IEEE (2015)Google Scholar
  3. 3.
    Ho, W., Xu, X., Dey, P.K.: Multi-criteria decision making approaches for supplier evaluation and selection: a literature review. Eur. J. Oper. Res. 202(1), 16–24 (2010)CrossRefzbMATHGoogle Scholar
  4. 4.
    Subramanian, N., Ramanathan, R.: A review of applications of analytic hierarchy process in operations management. Int. J. Prod. Econ. 138(2), 215–241 (2012)CrossRefGoogle Scholar
  5. 5.
    Millet, I., Saaty, T.L.: On the relativity of relative measures accommodating both rank preservation and rank reversals in the AHP. Eur. J. Oper. Res. 121(1), 205–212 (2000)CrossRefzbMATHGoogle Scholar
  6. 6.
    Triantaphyllou, E., Mann, S.H.: Using the analytic hierarchy process for decision making in engineering applications: some challenges. Int. J. Ind. Eng.: Appl. Pract. 2(1), 35–44 (1995)Google Scholar
  7. 7.
    Triantaphyllou, E.: Two new cases of rank reversals when the AHP and some of its additive variants are used that do not occur with the multiplicative AHP. J. Multi Criteria Decis. Anal. 10(1), 11–25 (2001)CrossRefzbMATHGoogle Scholar
  8. 8.
    Belton, V., Gear, T.: On a short-coming of Saaty’s method of analytic hierarchies. Omega 11(3), 228–230 (1983)CrossRefGoogle Scholar
  9. 9.
    Dyer, J.S.: Remarks on the analytic hierarchy process. Manag. Sci. 36(3), 249–258 (1990)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Dyer, J.S.: A clarification of remarks on the analytic hierarchy process. Manag. Sci. 36(3), 274–275 (1990)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Harker, P.T., Vagas, L.G.: The theory of ratio scale estimation: saaty’s analytic hierarchy proces. Manag. Sci. 33, 1383–1403 (1987)CrossRefGoogle Scholar
  12. 12.
    Harker, P.T., Vargas, L.G.: Reply to remarks on the analytic hierarchy process by J.S. Dyer. Manag. Sci. 36, 269–273 (1990)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Leung, L.C., Cao., D.: On the efficacy of modeling multi-attribute decision problems using AHP and Sinarchy. Eur. J. Oper. Res. 132, 39–49 (2001)Google Scholar
  14. 14.
    Saaty, T.L.: Axiomatic foundation of the analytic hierarchy process. Manag. Sci. 32, 841–855 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Saaty, T.L., Vargas, L.G., Wendell, R.E.: Assessing attribute weights by ratios. Omega 11, 9–13 (1983)CrossRefGoogle Scholar
  16. 16.
    Forman, E.H.: AHP is intended for more than expected value calculations. Decis. Sci. 36, 671–673 (1990)Google Scholar
  17. 17.
    Saaty, T.L.: Rank generation, preservation, and reversal in the analytic hierarchy decision process. Decis. Sci. 18, 157–177 (1987)CrossRefGoogle Scholar
  18. 18.
    Saaty, T.L.: Decision making, new information, ranking and structure. Math. Model. 8, 125–132 (1987)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Saaty, T.L., Vargas, L.G.: The legitimacy of rank reversal. Omega 12(5), 513–516 (1984)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Schoner, B., Wedley, W.C., Choo, E.U.: A rejoinder to Forman on AHP, with emphasis on the requirements of composite ratio scales. Decis. Sci. 23, 509–517 (1992)CrossRefGoogle Scholar
  21. 21.
    Schoner, B., Wedley, W.C.: Ambiguous criteria weights in AHP: consequences and solutions. Decis. Sci. 20, 462–475 (1989)CrossRefGoogle Scholar
  22. 22.
    Schoner, B., Wedley, W.C., Choo, E.U.: A unified approach to AHP with linking pins. Eur. J. Oper. Res. 64, 384–392 (1993)CrossRefGoogle Scholar
  23. 23.
    Barzilai, J., Golany, B.: AHP rank reversal, normalization and aggregation rules. INFOR 32(2), 57–63 (1994)zbMATHGoogle Scholar
  24. 24.
    Lootsma, F.A.: Scale sensitivity in the multiplicative AHP and SMART. J. Multi-Criteria Decis. Anal. 2, 87–110 (1993)CrossRefzbMATHGoogle Scholar
  25. 25.
    Barzilai, J., Lootsma, F.A.: Power relations and group aggregation in the multiplicative AHP and SMART. J. Multi-Criteria Decis. Anal. 6, 155–165 (1997)CrossRefzbMATHGoogle Scholar
  26. 26.
    Vargas, L.G.: Why the multiplicative AHP is invalid: a practical example. J. Multi-Criteria Decis. Anal. 6(3), 169–170 (1997)CrossRefGoogle Scholar
  27. 27.
    Wang, Y.M., Elhag, T.M.: An approach to avoiding rank reversal in AHP. Decis. Support Syst. 42(3), 1474–1480 (2006)CrossRefGoogle Scholar
  28. 28.
    Piegat, A., Sałabun, W.: Identification of a multicriteria decision-making model using the characteristic objects method. Appl. Comput. Intell. Soft Comput. (2014)Google Scholar
  29. 29.
    Piegat, A., Sałabun, W.: Nonlinearity of human multi-criteria in decision-making. J. Theor. Appl. Comput. Sci. 6(3), 36–49 (2012)Google Scholar
  30. 30.
    Piegat, A., Sałabun, W.: Comparative analysis of MCDM methods for assessing the severity of chronic liver disease. In: Artificial Intelligence and Soft Computing, pp. 228-238. Springer International Publishing (2015)Google Scholar
  31. 31.
    Sałabun, W.: Application of the fuzzy multi-criteria decision-making method to identify nonlinear decision models. Int. J. Comput. Appl. 89(15), 1–6 (2014)Google Scholar
  32. 32.
    Sałabun, W.: Reduction in the number of comparisons required to create matrix of expert judgment in the comet method. Manag. Prod. Eng. Rev. 5(3), 62–69 (2014)Google Scholar
  33. 33.
    Sałabun, W.: The characteristic objects method: a new distance based approach to multicriteria decision making problems. J. Multi Criteria Decis. Anal. 22(1–2), 37–50 (2015)CrossRefGoogle Scholar
  34. 34.
    Sałabun, W.: The use of fuzzy logic to evaluate the nonlinearity of human multi-criteria used in decision making. Przeglad Elektrotechniczny (Electrical Review) 88(10b), 235–238 (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Wojciech Sałabun
    • 1
    Email author
  • Paweł Ziemba
    • 2
  • Jarosław Wątróbski
    • 1
  1. 1.West Pomeranian University of TechnologySzczecinPoland
  2. 2.The Jacob of Paradyż University of Applied Sciences in Gorzów WielkopolskiGorzów WielkopolskiPoland

Personalised recommendations