Intransitivity in Inconsistent Judgments

  • Amir Homayoun Sarfaraz
  • Hamed Maleki
Part of the Studies in Computational Intelligence book series (SCI, volume 381)


In this paper we address one type of criticisms of the AHP. This is about inconsistent judgments and their effect on aggregating such judgments or on deriving priorities from them. Intransitivity is possible when the original AHP or REMBRANDT are used. A numerical example is examined using the original AHP and REMBRANDT to demonstrate intransitivity. This example shows that intransitivity is possible when inconsistent pairwise comparisons are used.


Analytic Hierarchy Process Pairwise Comparison Matrix Criterion Alternative Preference Intensity Rank Reversal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Barzilai, J., Lootsma, F.: Power Relations and Group Aggregation in the Multiplicative AHP and SMART. Journal of Multi-Criteria Decision Analysis 6, 155–165 (1997)zbMATHCrossRefGoogle Scholar
  2. 2.
    Fishburn, P.: Nontransitive Preferences in Decision Theory. Journal of Risk and Uncertainty 4, 113–134 (1991)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Kuhn, S.T.: The Structure of Scientific Revolution. University of Chicago Press (1962)Google Scholar
  4. 4.
    Lootsma, F., Mensch, T., Vos, F.: Multi-criteria analysis and budget reallocation in long-term research planning. European Journal of Operational Research 47, 293–305 (1990)CrossRefGoogle Scholar
  5. 5.
    Lootsma, F.: The REMBRANDT system for multi-criteria decision analysis via pairwise comparisons or direct rating. Report 92-05, Faculty of Technical Mathematics and Informatics (1992)Google Scholar
  6. 6.
    Lootsma, F.: Scale Sensitivity in he Multiplicative AHP and SMART. Journal of Multi-Criteria Decision Analysis 2, 87–110 (1993)zbMATHCrossRefGoogle Scholar
  7. 7.
    Luce, R., Raifa, H.: Games and Decisions. John Wiley and Sons, Inc., New York (1957)zbMATHGoogle Scholar
  8. 8.
    Olson, D., Fliedner, G., Currie, K.: Comparison of the REMBRANDT system with analytic hierarchy process. European Journal of Operational Research 82, 522–539 (1995)zbMATHCrossRefGoogle Scholar
  9. 9.
    Saaty, T.: A scaling method for priorities in hierarchical structures. Journal of Mathematical Psychology 15, 234–281 (1977)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Saaty, T.: The Analytic hierarchy process. McGraw-Hill, New York (1980)zbMATHGoogle Scholar
  11. 11.
    Saaty, T.: What is the analytic hierarchy process? In: Mitra, G. (ed.) Mathematical Models for Decision Support, pp. 109–122. Springer, Berlin (1988)Google Scholar
  12. 12.
    Saaty, T.: Physics as a decision theory. European Journal of Operational Research 48, 98–104 (1990)CrossRefGoogle Scholar
  13. 13.
    Saaty, T.: Highlights and critical points in the theory and application of the analytic hierarchy process. European Journal of Operational Research 74, 426–447 (1994)zbMATHCrossRefGoogle Scholar
  14. 14.
    Saaty, T.: Decision making for leaders. RWS Publication, Pittsburgh (1995)Google Scholar
  15. 15.
    Saaty, T., Hu, G.: Ranking by Eigenvector Versus Other Methods in the Aanalytic Hierarchy Process. Appl. Math. Lett., 121–125 (1998)Google Scholar
  16. 16.
    Sugihara, K., Ranaka, H.: Interval evaluations in the analytic hierarchy process by possibility analysis. Computational Intelligence 17(3), 567–579 (2001)CrossRefGoogle Scholar
  17. 17.
    Tversky, A.: Intransitivity of Preferences. Psychological Review 76, 31–48 (1969)CrossRefGoogle Scholar
  18. 18.
    Van Den Honert, R.: Stochastic pairwise comparative judgments and direct ratings of alternatives in the REMBRANDT system. Journal of Multi-Criteria Decision Analysis 7, 87–97 (1998)zbMATHCrossRefGoogle Scholar
  19. 19.
    Vargas, L.: Why the multiplicative AHP is invalid: A practical counterexample. Journal of Multi-Criteria Decision Analysis 6, 169–170 (1997)CrossRefGoogle Scholar
  20. 20.
    Wijnmalen, D.J., Wedley, W.: Correcting Illegitimate Rank Reversals: Proper Adjustment. Journal of Multi-Criteria Decision Analysis, 135–141 (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Amir Homayoun Sarfaraz
    • 1
  • Hamed Maleki
    • 2
  1. 1.Industrial engineering faculty, South Tehran BranchIslamic Azad UniversityTehranIran
  2. 2.Young Researchers Club, South Tehran BranchIslamic Azad UniversityTehranIran

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