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Acceptable consistency of aggregated comparison matrices in analytic hierarchy process

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  • Grošelj, Petra
  • Zadnik Stirn, Lidija
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    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal European Journal of Operational Research.

    Volume (Year): 223 (2012)
    Issue (Month): 2 ()
    Pages: 417-420

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    Handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:417-420

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    Web page: http://www.elsevier.com/locate/eor

    Related research

    Keywords: Multiple criteria analysis; Group decision making; Analytic Hierarchy Process (AHP); Consistency;

    References

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    1. Lin, Robert & Lin, Jennifer Shu-Jen & Chang, Jason & Tang, Didos & Chao, Henry & Julian, Peter C, 2008. "Note on group consistency in analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 190(3), pages 672-678, November.
    2. Xu, Z., 2000. "On consistency of the weighted geometric mean complex judgement matrix in AHP," European Journal of Operational Research, Elsevier, vol. 126(3), pages 683-687, November.
    3. Cortés-Aldana, Félix Antonio & García-Melón, Mónica & Fernández-de-Lucio, Ignacio & Aragonés-Beltrán, Pablo & Poveda-Bautista, Rocío, 2009. "University objectives and socioeconomic results: A multicriteria measuring of alignment," European Journal of Operational Research, Elsevier, vol. 199(3), pages 811-822, December.
    4. Altuzarra, Alfredo & Moreno-Jimenez, Jose Maria & Salvador, Manuel, 2007. "A Bayesian priorization procedure for AHP-group decision making," European Journal of Operational Research, Elsevier, vol. 182(1), pages 367-382, October.
    5. Rabelo, Luis & Eskandari, Hamidreza & Shaalan, Tarek & Helal, Magdy, 2007. "Value chain analysis using hybrid simulation and AHP," International Journal of Production Economics, Elsevier, vol. 105(2), pages 536-547, February.
    6. Aczel, J. & Alsina, C., 1986. "On synthesis of judgements," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 333-339.
    7. Forman, Ernest & Peniwati, Kirti, 1998. "Aggregating individual judgments and priorities with the analytic hierarchy process," European Journal of Operational Research, Elsevier, vol. 108(1), pages 165-169, July.
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    Cited by:
    1. 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.
    2. 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.
    3. 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.
    4. Zhü, Kèyù, 2014. "Fuzzy analytic hierarchy process: Fallacy of the popular methods," European Journal of Operational Research, Elsevier, vol. 236(1), pages 209-217.
    5. 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.

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