Journal
JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY
Volume 69, Issue 7, Pages 1114-1124Publisher
TAYLOR & FRANCIS LTD
DOI: 10.1080/01605682.2017.1390533
Keywords
Decision analysis; decision support systems; multi-objective; non-linear programming; optimization
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This paper focuses on specific rank reversal phenomena in optimization methods (the least squares method, the chi-square method, etc.) designed to derive preference weights of alternatives from pairwise comparison matrices in the Analytic Hierarchy Process. It is preferable that the most irrelevant alternative had no effect on the ranking of the other alternatives. Unfortunately, it appears that, for many methods, most irrelevant alternatives tend to dictate the rank order of all the remaining alternatives. Respectively, adding some irrelevant alternative may turn the most important alternative into an unimportant one and conversely. We classify the optimization methods with respect to the dependence of irrelevant alternatives and specify all possible dictatorial methods, which provide the absolute dictate of very irrelevant alternatives, and all methods, which are free from the dictate of such alternatives. For the dictatorial methods, we propose weight function modifications, which prevent the influence of irrelevant alternatives. We show that without the modification, dictatorial methods can add confusion and false recommendations in the decision-making process even in the most ordinary decision-making situations.
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