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Rank reversal properties of multicriteria decision making models

Li, Shi (2010)
M.Phil. thesis, University of Birmingham.

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Abstract

Decision making problems in modern society are very important however complex. Therefore, they require strong solving techniques to handle. The AHP method attracts a lot attention for its advantages and has a very well structured methodology, while the PROMETHEE method of the European school is also widely accepted. Pairwise comparison is one of the fundamental methods for AHP, with its methodology track back to the definition of Perron-Frobenius theorem. Perron-Fronbenius explained the most fundamental structure of arbitrary pairwise comparison. The distributive model and the ideal model are widely accepted as a powerful tool in AHP multicriteria decision making problems based on pairwise comparison. In these models, it might happen that by introducing a new alternative, the original order of alternatives will change. Moreover, it is possible to introduce a new alternative, such that the order of the original alternatives will be given by ’almost any’ criterion. In the latter part of this paper, we then give the detailed proofs based on these two models, and some examples which shows rank reversal caused by this new alternative could be harmful. As a continuous thinking of this case, in the second part, detailed proof are given about a method from Dr. S. Z. Nemeth, by defining the ’maximal box’ in avoid causing rank reversal. These would then be followed with real life examples and results by using the software known as Experts’ Choice, which consist the the rest part of this project.

Type of Work:M.Phil. thesis.
Supervisor(s):Nemeth, Sandor Zoltan
School/Faculty:Colleges (2008 onwards) > College of Engineering & Physical Sciences
Department:School of Mathematics
Subjects:QA Mathematics
Institution:University of Birmingham
ID Code:740
This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.
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