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Checking and adjusting order-consistency of linguistic pairwise comparison matrices for getting transitive preference relations

Author

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  • Wu-E Yang

    (Hunan University
    Central South University of Forestry and Technology
    Hunan Provincial Engineering Laboratory of Risk Management and Control Techniques for the Innovative Enterprises)

  • Chao-Qun Ma

    (Hunan University)

  • Zhi-Qiu Han

    (Central South University)

  • Wen-Jun Chen

    (Central South University of Forestry and Technology
    Hunan Provincial Engineering Laboratory of Risk Management and Control Techniques for the Innovative Enterprises)

Abstract

Linguistic pairwise comparison matrices for decision-making need to be (strongly) order-consistent, which means the judgments should be (strongly) transitive. We introduce the equivalent conditions of (strong) transitivity by using route matrices and digraphs and develop an adjustment procedure to help decision makers correcting the inconsistency. The conclusion can extend to other ordinal-scaled or numerical comparison matrices as well.

Suggested Citation

  • Wu-E Yang & Chao-Qun Ma & Zhi-Qiu Han & Wen-Jun Chen, 2016. "Checking and adjusting order-consistency of linguistic pairwise comparison matrices for getting transitive preference relations," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(3), pages 769-787, July.
    • Handle: RePEc:spr:orspec:v:38:y:2016:i:3:d:10.1007_s00291-015-0417-8
    DOI: 10.1007/s00291-015-0417-8
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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. Kou, Gang & Ergu, Daji & Shang, Jennifer, 2014. "Enhancing data consistency in decision matrix: Adapting Hadamard model to mitigate judgment contradiction," European Journal of Operational Research, Elsevier, vol. 236(1), pages 261-271.
    3. Yang, Wu-E & Wang, Jian-Qiang, 2013. "Multi-criteria semantic dominance: A linguistic decision aiding technique based on incomplete preference information," European Journal of Operational Research, Elsevier, vol. 231(1), pages 171-181.
    4. 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.
    5. Jian-qiang Wang & Juan-juan Peng & Hong-yu Zhang & Tao Liu & Xiao-hong Chen, 2015. "An Uncertain Linguistic Multi-criteria Group Decision-Making Method Based on a Cloud Model," Group Decision and Negotiation, Springer, vol. 24(1), pages 171-192, January.
    6. Herrera-Viedma, E. & Herrera, F. & Chiclana, F. & Luque, M., 2004. "Some issues on consistency of fuzzy preference relations," European Journal of Operational Research, Elsevier, vol. 154(1), pages 98-109, April.
    7. 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.
    8. Aguaron, Juan & Escobar, Maria Teresa & Moreno-Jimenez, Jose Maria, 2003. "Consistency stability intervals for a judgement in AHP decision support systems," European Journal of Operational Research, Elsevier, vol. 145(2), pages 382-393, March.
    9. Leung, L. C. & Cao, D., 2000. "On consistency and ranking of alternatives in fuzzy AHP," European Journal of Operational Research, Elsevier, vol. 124(1), pages 102-113, July.
    10. Escobar, M. T. & Aguaron, J. & Moreno-Jimenez, J. M., 2004. "A note on AHP group consistency for the row geometric mean priorization procedure," European Journal of Operational Research, Elsevier, vol. 153(2), pages 318-322, March.
    11. Yoram Wind & Thomas L. Saaty, 1980. "Marketing Applications of the Analytic Hierarchy Process," Management Science, INFORMS, vol. 26(7), pages 641-658, July.
    12. Larichev, O. I. & Moshkovich, H. M., 1995. "ZAPROS-LM -- A method and system for ordering multiattribute alternatives," European Journal of Operational Research, Elsevier, vol. 82(3), pages 503-521, May.
    13. Doukas, Haris, 2013. "Modelling of linguistic variables in multicriteria energy policy support," European Journal of Operational Research, Elsevier, vol. 227(2), pages 227-238.
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    Cited by:

    1. Fu, Chao & Chang, Wenjun & Xue, Min & Yang, Shanlin, 2019. "Multiple criteria group decision making with belief distributions and distributed preference relations," European Journal of Operational Research, Elsevier, vol. 273(2), pages 623-633.

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