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The consistency index in reciprocal matrices: Comparison of deterministic and statistical approaches

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  • Vargas, Luis G.

Abstract

When checking the inconsistency level of a positive reciprocal matrix Saaty uses a deterministic criterion based on two parameters, a benchmark (the average), and a consistency level, usually 10%. Using results from a simulation experiment with 100,000 positive random reciprocal matrices of size varying from 3 to 15, we developed a probabilistic criterion and compare it to Saaty's index. We found that if a positive reciprocal matrix is consistent according to the deterministic criterion is also consistent according to the probabilistic criterion only if we accept a higher than usual probability of Type I error. Reducing this error implies that the benchmark must be a small percentile of the probability distribution of the consistency index.

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  • Vargas, Luis G., 2008. "The consistency index in reciprocal matrices: Comparison of deterministic and statistical approaches," European Journal of Operational Research, Elsevier, vol. 191(2), pages 454-463, December.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:2:p:454-463
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    References listed on IDEAS

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    1. Thomas L. Saaty, 1986. "Axiomatic Foundation of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 32(7), pages 841-855, July.
    2. 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. Changsheng Lin & Gang Kou & Daji Ergu, 2013. "An improved statistical approach for consistency test in AHP," Annals of Operations Research, Springer, vol. 211(1), pages 289-299, December.
    3. A. M. Alamdari & Y. Jabarzadeh & B. Adams & D. Samson & S. Khanmohammadi, 2023. "An analytic network process model to prioritize supply chain risks in green residential megaprojects," Operations Management Research, Springer, vol. 16(1), pages 141-163, March.
    4. Zikang Hao & Mengmeng Zhang & Kerui Liu & Xiaodan Zhang & Haoran Jia & Ping Chen, 2022. "Where Is the Way Forward for New Media Empowering Public Health? Development Strategy Options Based on SWOT-AHP Model," IJERPH, MDPI, vol. 19(19), pages 1-19, October.
    5. 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.
    6. 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.
    7. Liu, Fang & Zou, Shu-Cai & Li, Qing, 2020. "Deriving priorities from pairwise comparison matrices with a novel consistency index," Applied Mathematics and Computation, Elsevier, vol. 374(C).

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