# Right and left eigenvector inconsistency in analytic hierarchy process (AHP)

 Author: Tung, Sheung-lai George Title: Right and left eigenvector inconsistency in analytic hierarchy process (AHP) Degree: M.Sc. Year: 1997 Subject: Decision making -- Mathematical modelsHong Kong Polytechnic University -- Dissertations Department: Multi-disciplinary Studies Pages: v, 103 leaves : ill. ; 30 cm Language: English InnoPac Record: http://library.polyu.edu.hk/record=b1398656 URI: http://theses.lib.polyu.edu.hk/handle/200/582 Abstract: The Analytic Hierarchy Process (AHP) is a systems analysis technique which was developed by T.L. Saaty in 1977. It is a very powerful tool for solving decision problems by considering tangible and intangible factors simultaneously. The mathematics behind the AHP is actually the well-known eigenvalue and eigenvector problem together with some manipulations in matrix algebra. In Saaty's works, only the right eigenvectors were used. However, the use of the left eigenvectors should be equally justified. Apparently, for ranking a set of alternatives in a decision problem, both of the two eigenvector approaches should yield the same result. Unfortunately, it is often not the case and the reason for the inconsistency is still not certain. This fundamental problem was observed firstly by Johnson et al. in 1979. In addition to Saaty's AHP method, a new approach to the AHP decision-making known as the Modified Analytic Hierarchy Process was devised by Donegan et al. in 1992. As claimed in their papers, the inconsistent problem could be effectively reduced by using the new methodology in the AHP analysis. This work is an attempt to test the two AHP methods (i.e., Saaty's AHP and Modified AHP) by using both the right and left eigenvector approaches for 42 proposed AHP models involving a total of 294 reciprocal matrices. It also tries to identify the best eigenvector approach as well as the best AHP method and suggest any modification that may be possible to improve the result of the AHP.

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