Lundy, M, Siraj, S orcid.org/0000-0002-7962-9930 and Greco, S (2017) The mathematical equivalence of the "spanning tree" and row geometric mean preference vectors and its implications for preference analysis. European Journal of Operational Research, 257 (1). pp. 197-208. ISSN 0377-2217
Abstract
Pairwise comparison is a widely used approach to elicit comparative judgements from a decision maker (DM), and there are a number of methods that can be used to then subsequently derive a consistent preference vector from the DM's judgements. While the most widely used method is the eigenvector method, the row geometric mean approach has gained popularity due to its mathematical properties and its ease of implementation. In this paper, we discuss a spanning tree method and prove the mathematical equivalence of its preference vector to that of the row geometric mean approach. This is an important finding due to the fact that it identifies an approach for generating a preference vector which has the mathematical properties of the row geometric mean preference vector, and yet, in its entirety, the spanning tree method has more to offer than the row geometric mean method, in that, it is inherently applicable to incomplete sets of pairwise comparison judgements, and also facilitates the use of statistical and visual techniques to gain insights into inconsistency in the DM's judgements.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2016 Elsevier B.V. All rights reserved. This is an author produced version of a paper published in European Journal of Operational Research. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Decision analysis; Pairwise comparisons; Multiple criteria analysis; Graph theory; Spanning trees |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Business (Leeds) > Management Division (LUBS) (Leeds) The University of Leeds > Faculty of Business (Leeds) > Management Division (LUBS) (Leeds) > Management Division Decision Research (LUBS) |
Depositing User: | Symplectic Publications |
Date Deposited: | 21 Jul 2016 10:19 |
Last Modified: | 27 Jul 2018 00:38 |
Published Version: | https://doi.org/10.1016/j.ejor.2016.07.042 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.ejor.2016.07.042 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:102699 |