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An improved statistical approach for consistency test in AHP

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  • Changsheng Lin
  • Gang Kou
  • Daji Ergu

Abstract

The pair-wise comparison matrix (PCM) is widely used in multi-criteria decision making methods. If the PCM is inconsistent, the resulting priority vector is not reliable. Hence, it is necessary to measure the level of the inconsistency of the PCM. There are two approaches for testing the consistency of the PCM: deterministic approaches and statistical or stochastic approaches. In this paper, an improved statistical approach to test the consistency of the PCM is proposed, which combines hypothesis test and maximum likelihood estimation. The proposed statistical approach is flexible and reliable because it sets a suitable significance level according to different situations. Two numerical examples are introduced to illustrate the proposed statistical approach. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:211:y:2013:i:1:p:289-299:10.1007/s10479-013-1413-5
    DOI: 10.1007/s10479-013-1413-5
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    1. Hauser, David & Tadikamalla, Pandu, 1996. "The Analytic Hierarchy Process in an uncertain environment: A simulation approach," European Journal of Operational Research, Elsevier, vol. 91(1), pages 27-37, May.
    2. Yi Peng & Gang Kou & Guoxun Wang & Wenshuai Wu & Yong Shi, 2011. "Ensemble Of Software Defect Predictors: An Ahp-Based Evaluation Method," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 187-206.
    3. Vargas, Luis G., 1990. "An overview of the analytic hierarchy process and its applications," European Journal of Operational Research, Elsevier, vol. 48(1), pages 2-8, September.
    4. L. Sun & B. S. Greenberg, 2006. "Multicriteria Group Decision Making: Optimal Priority Synthesis from Pairwise Comparisons," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 317-339, August.
    5. Hovanov, Nikolai V. & Kolari, James W. & Sokolov, Mikhail V., 2008. "Deriving weights from general pairwise comparison matrices," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 205-220, March.
    6. Escobar, M. T. & Moreno-Jimenez, J. M., 2000. "Reciprocal distributions in the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 123(1), pages 154-174, May.
    7. Ergu, Daji & Kou, Gang & Peng, Yi & Shi, Yong, 2011. "A simple method to improve the consistency ratio of the pair-wise comparison matrix in ANP," European Journal of Operational Research, Elsevier, vol. 213(1), pages 246-259, August.
    8. Peng, Yi & Kou, Gang & Wang, Guoxun & Shi, Yong, 2011. "FAMCDM: A fusion approach of MCDM methods to rank multiclass classification algorithms," Omega, Elsevier, vol. 39(6), pages 677-689, December.
    9. 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.
    10. Michele Bernasconi & Christine Choirat & Raffaello Seri, 2010. "The Analytic Hierarchy Process and the Theory of Measurement," Management Science, INFORMS, vol. 56(4), pages 699-711, April.
    11. Karapetrovic, Stanislav & Rosenbloom, E. S., 1999. "A quality control approach to consistency paradoxes in AHP," European Journal of Operational Research, Elsevier, vol. 119(3), pages 704-718, December.
    12. 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.
    13. 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.
    14. P Ji & R Jiang, 2003. "Scale transitivity in the AHP," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(8), pages 896-905, August.
    15. 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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    3. Juan Aguarón & María Teresa Escobar & José María Moreno-Jiménez, 2016. "The precise consistency consensus matrix in a local AHP-group decision making context," Annals of Operations Research, Springer, vol. 245(1), pages 245-259, October.
    4. Kun Chen & Gang Kou & J. Michael Tarn & Yan Song, 2015. "Bridging the gap between missing and inconsistent values in eliciting preference from pairwise comparison matrices," Annals of Operations Research, Springer, vol. 235(1), pages 155-175, December.
    5. Mohd. Sadiq & Mohd. Sadim & Azra Parveen, 2021. "Applying statistical approach to check the consistency of pairwise comparison matrices during software requirements prioritization process," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 12(3), pages 451-460, June.
    6. Al-Kayiem, Hussain H. & Aja, Ogboo Chikere, 2016. "Historic and recent progress in solar chimney power plant enhancing technologies," Renewable and Sustainable Energy Reviews, Elsevier, vol. 58(C), pages 1269-1292.
    7. Ágoston, Kolos Csaba & Csató, László, 2022. "Inconsistency thresholds for incomplete pairwise comparison matrices," Omega, Elsevier, vol. 108(C).
    8. Idil Yavuz & Orrin Cooper, 2017. "A dynamic clustering method to improve the coherency of an ANP Supermatrix," Annals of Operations Research, Springer, vol. 254(1), pages 507-531, July.
    9. Meimei Xia & Jian Chen & Juliang Zhang, 2015. "Multi-criteria decision making based on relative measures," Annals of Operations Research, Springer, vol. 229(1), pages 791-811, June.
    10. 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.
    11. 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.
    12. Pietro Amenta & Alessio Ishizaka & Antonio Lucadamo & Gabriella Marcarelli & Vijay Vyas, 2020. "Computing a common preference vector in a complex multi-actor and multi-group decision system in Analytic Hierarchy Process context," Annals of Operations Research, Springer, vol. 284(1), pages 33-62, January.
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    14. Pelin Toktaş & Gülin Feryal Can, 2019. "Stochastic KEMIRA-M Approach with Consistent Weightings," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(03), pages 793-831, May.

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