A sensitivity analysis in MCDM problems: A statistical approach
This study provides a model for result consistency evaluation of multi-criteria decision-making (MDM) methods and selection of the optimal one. The study presents the results of an analysis of the sensitivity of decision-making based on the rank methods: SAW, MOORA, VIKOR, COPRAS, CODAS, TOPSIS, D’IDEAL, MABAC, PROMETHEE-I,II, ORESTE-II with variations in the elements in the decision matrix within a given error (imprecision). It is suggested to use multiple simulation of the elements estimations of the decision matrix within a given error for calculating the ranks of alternatives, which allows obtaining statistical estimates of ranks. Based on the statistics of simulations, decision-making can be carried out not only on the alternatives statistics having rank I but also on the statistics of alternatives having the largest total I and II rank or I, II and III ranks. This is especially true when the difference in rank values is not large and is distributed evenly among the first three ranks. The calculations results for the task of selecting the adequate location of 8 objects by 11 criteria are presented here. The main result shows that the alternatives having I, II and III ranks for some ranking methods are not distinguishable within the selected error value of the elements in the decision matrix. A quantitative analysis can only narrow the number of effective alternatives for a final decision. A statistical analysis makes the number of options estimation possible in which an alternative has a priority. Additional criteria that take into account both aggregate priorities and the availability of possible priorities for other alternatives with small variations in the decision matrix provide additional important information for the decision-maker.
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