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Some notes on the properties of inconsistency indices in pairwise comparisons

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  • Jiří Mazurek

Abstract

Pairwise comparisons are an important tool of modern (multiple criteria) decision making. Since human judgments are often inconsistent, many studies have focused on the means of expressing and measuring this inconsistency, and several inconsistency indices have been proposed as an alternative to Saaty’s inconsistency index, CI, and consistency ratio, CR, for reciprocal pairwise comparison matrices. The aims of this paper are threefold: firstly, a row inconsistency index (RIC) is proposed and the properties of this index are examined. Secondly, a comparison of selected inconsistency indices for a corner pairwise comparison matrix is provided. Last, but not least, another axiom about the upper bound on the value of an inconsistency index is postulated, and a set of selected inconsistency indices is examined with respect to this axiom. Numerical examples complete the paper.

Suggested Citation

  • Jiří Mazurek, 2018. "Some notes on the properties of inconsistency indices in pairwise comparisons," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 28(1), pages 27-42.
    • Handle: RePEc:wut:journl:v:1:y:2018:p:27-42:id:1340
    DOI: 10.5277/ord180102
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    References listed on IDEAS

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    1. Aguaron, Juan & Moreno-Jimenez, Jose Maria, 2003. "The geometric consistency index: Approximated thresholds," European Journal of Operational Research, Elsevier, vol. 147(1), pages 137-145, May.
    2. Bana e Costa, Carlos A. & Vansnick, Jean-Claude, 2008. "A critical analysis of the eigenvalue method used to derive priorities in AHP," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1422-1428, June.
    3. James S. Dyer, 1990. "Remarks on the Analytic Hierarchy Process," Management Science, INFORMS, vol. 36(3), pages 249-258, March.
    4. Alessio Ishizaka & Markus Lusti, 2006. "How to derive priorities in AHP: a comparative study," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 14(4), pages 387-400, December.
    5. Matteo Brunelli & Michele Fedrizzi, 2015. "Axiomatic properties of inconsistency indices for pairwise comparisons," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 66(1), pages 1-15, January.
    6. Matteo Brunelli & Luisa Canal & Michele Fedrizzi, 2013. "Inconsistency indices for pairwise comparison matrices: a numerical study," Annals of Operations Research, Springer, vol. 211(1), pages 493-509, December.
    7. James S. Dyer, 1990. "A Clarification of "Remarks on the Analytic Hierarchy Process"," Management Science, INFORMS, vol. 36(3), pages 274-275, March.
    8. Stein, William E. & Mizzi, Philip J., 2007. "The harmonic consistency index for the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 177(1), pages 488-497, February.
    9. Kou, Gang & Lin, Changsheng, 2014. "A cosine maximization method for the priority vector derivation in AHP," European Journal of Operational Research, Elsevier, vol. 235(1), pages 225-232.
    10. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
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    Cited by:

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    2. Vladimír Bureš & Jiří Cabal & Pavel Čech & Karel Mls & Daniela Ponce, 2020. "The Influence of Criteria Selection Method on Consistency of Pairwise Comparison," Mathematics, MDPI, vol. 8(12), pages 1-13, December.
    3. Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez & Alberto Turón, 2020. "The Triads Geometric Consistency Index in AHP-Pairwise Comparison Matrices," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
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    5. Joseph Gogodze, 2019. "Innovative advantages ranking. A new approach," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(1), pages 5-15.

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