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Acceptable consistency of aggregated comparison matrices in analytic hierarchy process

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  • Grošelj, Petra
  • Zadnik Stirn, Lidija

Abstract

The analytic hierarchy process is a method for solving multiple criteria decision problems, as well as group decision making. The weighted geometric mean method is appropriate when aggregation of individual judgements is used. This paper presents a new proof which confirms the property that if the comparison matrices of all decision makers are of acceptable consistency, then the weighted geometric mean complex judgement matrix (WGMCJM) also is of acceptable consistency. This property was presented and first proved by Xu (2000), but Lin et al. (2008) rejected the proof. We also discuss under what conditions the WGMCJM is of acceptable consistency when not all comparison matrices of decision makers are of acceptable consistency. For this case we determine the sufficient condition for the WGMCJM to be of acceptable consistency and provide numerical examples. For a special case of two decision makers with 3×3 comparison matrices we find out some additional conditions for the WGMCJM to be of acceptable consistency.

Suggested Citation

  • Grošelj, Petra & Zadnik Stirn, Lidija, 2012. "Acceptable consistency of aggregated comparison matrices in analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 223(2), pages 417-420.
  • Handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:417-420
    DOI: 10.1016/j.ejor.2012.06.016
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    References listed on IDEAS

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    Cited by:

    1. Dong, Qingxing & Cooper, Orrin, 2016. "A peer-to-peer dynamic adaptive consensus reaching model for the group AHP decision making," European Journal of Operational Research, Elsevier, vol. 250(2), pages 521-530.
    2. Zhu, Bin & Xu, Zeshui, 2014. "Analytic hierarchy process-hesitant group decision making," European Journal of Operational Research, Elsevier, vol. 239(3), pages 794-801.
    3. Zhü, Kèyù, 2014. "Fuzzy analytic hierarchy process: Fallacy of the popular methods," European Journal of Operational Research, Elsevier, vol. 236(1), pages 209-217.
    4. Fontana, Veronika & Radtke, Anna & Bossi Fedrigotti, Valérie & Tappeiner, Ulrike & Tasser, Erich & Zerbe, Stefan & Buchholz, Thomas, 2013. "Comparing land-use alternatives: Using the ecosystem services concept to define a multi-criteria decision analysis," Ecological Economics, Elsevier, vol. 93(C), pages 128-136.
    5. Brunelli, Matteo & Fedrizzi, Michele, 2015. "Boundary properties of the inconsistency of pairwise comparisons in group decisions," European Journal of Operational Research, Elsevier, vol. 240(3), pages 765-773.
    6. Yeh, Chung-Hsing & Xu, Yan, 2013. "Managing critical success strategies for an enterprise resource planning project," European Journal of Operational Research, Elsevier, vol. 230(3), pages 604-614.
    7. 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.
    8. Dong, Yucheng & Hong, Wei-Chiang & Xu, Yinfeng & Yu, Shui, 2013. "Numerical scales generated individually for analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 229(3), pages 654-662.
    9. Zhu, Bin & Xu, Zeshui, 2014. "Stochastic preference analysis in numerical preference relations," European Journal of Operational Research, Elsevier, vol. 237(2), pages 628-633.

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