A heuristics approach for computing the largest eigenvalue of a pairwise comparison matrix

2.50
Hdl Handle:
http://hdl.handle.net/10547/622052
Title:
A heuristics approach for computing the largest eigenvalue of a pairwise comparison matrix
Authors:
Nachiappan, Subramanian; Ramanathan, Ramakrishnan ( 0000-0002-8861-2209 )
Abstract:
Pairwise comparison matrices (PCMs) are widely used to capture subjective human judgements, especially in the context of the Analytic Hierarchy Process (AHP). Consistency of judgements is normally computed in AHP context in the form of consistency ratio (CR), which requires estimation of the largest eigenvalue (Lmax) of PCMs. Since many of these alternative methods do not require calculation of eigenvector, Lmax and hence the CR of a PCM cannot be easily estimated. We propose in this paper a simple heuristics for calculating Lmax without any need to use Eigenvector Method (EM). We illustrated the proposed procedure with larger size matrices. Simulation is used to compare the accuracy of the proposed heuristics procedure with actual Lmax for PCMs of various sizes. It has been found that the proposed heuristics is highly accurate, with errors less than 1%. The proposed procedure would avoid biases and help managers to make better decisions. The advantage of the proposed heuristics is that it can be easily calculated with simple calculations without any need for specialised mathematical procedures or software and is independent of the method used to derive priorities from PCMs.
Citation:
Nachiappan S, Ramanathan R (2016) 'A heuristics approach for computing the largest eigenvalue of a pairwise comparison matrix', International Journal of Operational Research.
Publisher:
Inderscience
Journal:
International Journal of Operational Research
Issue Date:
14-Mar-2017
URI:
http://hdl.handle.net/10547/622052
Type:
Article
Language:
en
ISSN:
1745-7645
Appears in Collections:
Business and management

Full metadata record

DC FieldValue Language
dc.contributor.authorNachiappan, Subramanianen
dc.contributor.authorRamanathan, Ramakrishnanen
dc.date.accessioned2017-03-14T13:40:09Z-
dc.date.available2017-03-14T13:40:09Z-
dc.date.issued2017-03-14-
dc.identifier.citationNachiappan S, Ramanathan R (2016) 'A heuristics approach for computing the largest eigenvalue of a pairwise comparison matrix', International Journal of Operational Research.en
dc.identifier.issn1745-7645-
dc.identifier.urihttp://hdl.handle.net/10547/622052-
dc.description.abstractPairwise comparison matrices (PCMs) are widely used to capture subjective human judgements, especially in the context of the Analytic Hierarchy Process (AHP). Consistency of judgements is normally computed in AHP context in the form of consistency ratio (CR), which requires estimation of the largest eigenvalue (Lmax) of PCMs. Since many of these alternative methods do not require calculation of eigenvector, Lmax and hence the CR of a PCM cannot be easily estimated. We propose in this paper a simple heuristics for calculating Lmax without any need to use Eigenvector Method (EM). We illustrated the proposed procedure with larger size matrices. Simulation is used to compare the accuracy of the proposed heuristics procedure with actual Lmax for PCMs of various sizes. It has been found that the proposed heuristics is highly accurate, with errors less than 1%. The proposed procedure would avoid biases and help managers to make better decisions. The advantage of the proposed heuristics is that it can be easily calculated with simple calculations without any need for specialised mathematical procedures or software and is independent of the method used to derive priorities from PCMs.en
dc.language.isoenen
dc.publisherInderscienceen
dc.rightsYellow - can archive pre-print (ie pre-refereeing)-
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.subjectmultiple criteria analysisen
dc.subjectpairwise comparison matrixen
dc.subjectEigenvector methoden
dc.subjecteigenvalueen
dc.subjectconsistency indexen
dc.titleA heuristics approach for computing the largest eigenvalue of a pairwise comparison matrixen
dc.typeArticleen
dc.identifier.journalInternational Journal of Operational Researchen
dc.date.updated2017-03-14T13:32:58Z-
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