Uncertainty and rank order in the analytic hierarchy process (original) (raw)
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This paper focuses on the need to evaluate the sustainability of Analytic hierarchy process at the Ranking of more than 10 alternatives. The proposed method is based on simulation modeling of the process of improving expert pair-wise comparison judgments. The represented method provides a stepwise improvement of the pair-wise comparison matrix transitivity. The average discrepancy and coincidence of ranks in multiple modeling are proposed as estimates of the rating stability. The application of the developed method was studied on a statistical sample formed according to the final tables of the England, Germany and Spain football championships. The method for determining probability of some alternatives ranks is developed. It is possible to modify the method for predicting the results of sports competitions and for the case of ranking with partially missing expert ratings.
Deriving Priorities the Alternatives in an Analytic Hierarchy Process
International Journal of Research, 2014
The data envelopment analysis (DEA) is a mathematical programming technique, which is used for evaluating relative efficiency of decision making units (DMUs). However, the DEA does not provide more information about the efficient DMUs. Recently, some researchers have been carried out in the background of using DEA models to generate local weights of alternatives from pairwise comparison matrices used in the analytic hierarchy process (AHP). In this paper, an application of a common set of weights is used for determining priorities in the AHP. First, we determine DEA efficient alternatives as DMUs. Then, these alternatives are ranked according to the efficiency score weighted by the common set of weights in the AHP. This application is applied successfully and the result is valid and assured. A numerical example is utilized to illustrate the capability of this procedure.
Journal of Applied Information Science, 2017
In this paper, we first reviews different measurement scales (Linear, Power, Geometric, Logarithmic, Root square, Inverse linear, and Balanced) adopted in Analytic Hierarchy Process (AHP). then, with reduction of different measurement scale ranges to: left position (i.e., for linear measurement scale: 1-3), middle position (4-6), right position (7-9), left & middle position (1-6), middle & right position (4-9), and perfect ranges (1-9), the effects of different measurement scale on priorities and discrimination level (to discriminate an important alternative from others) of alternatives are investigated. The findings of this paper reveal that first, in 39 possibilities out of 42 cases, the same ranking (A1>A2>A3) with different intensities were obtained, and in 3 possibilities rank reversal are happened. Next, the geometric measurement scale in all ranges and particularly in perfect range have the best performance in discriminating an important alternative than others. Moreover, only the left position and perfect ranges in the most of measurement scales have the best performance in discriminating an important alternative from others.