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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Aczel, J. & Alsina, C., 1986. "On synthesis of judgements," Socio-Economic Planning Sciences, Elsevier, vol. 20(6), pages 333-339.
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: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.