Acceptable consistency of aggregated comparison matrices in analytic hierarchy process
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.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Aczel, J. & Alsina, C., 1986. "On synthesis of judgements," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 333-339.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:223:y:2012:i:2:p:417-420. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.