Notes on order preservation and consistency in AHP

Konrad Kułakowski

European Journal of Operational Research, 2015, vol. 245, issue 1, 333-337

Abstract: The pairwise comparisons method is a convenient tool used when the relative order among different concepts (alternatives) needs to be determined. One popular implementation of the method is based on solving an eigenvalue problem for the pairwise comparisons matrix. In such cases the ranking result for the principal eigenvector of the pairwise comparisons matrix is adopted, while the eigenvalue is used to determine the index of inconsistency. A lot of research has been devoted to the critical analysis of the eigenvalue based approach. One of them is the work of Bana e Costa and Vansnick (2008). In their work, the authors define the conditions of order preservation (COP) and show that even for sufficiently consistent pairwise comparisons matrices, this condition cannot be met. The presented work defines more precise criteria for determining when the COP is met. To formulate the criteria, an error factor is used describing how far the input to the ranking procedure is from the ranking result. The relationship between the Saaty consistency index and COP is also discussed.

Keywords: Decision analysis; Pairwise comparisons method; AHP; Conditions of order preservation (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0377221715002039
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:245:y:2015:i:1:p:333-337

DOI: 10.1016/j.ejor.2015.03.010

Access Statistics for this article

European Journal of Operational Research is currently edited by Roman Slowinski, Jesus Artalejo, Jean-Charles. Billaut, Robert Dyson and Lorenzo Peccati

More articles in European Journal of Operational Research from Elsevier
Bibliographic data for series maintained by Catherine Liu ().