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