On Solving Multicriteria Decision Making Problems Based on Pairwise Comparisons

Problems known in the literature are considered for evaluating ratings of alternatives based on pairwise comparisons. To solve the problems, three methods are used, including the traditional method of of analysis of hierarchies by T. Saaty and the method of weighted geometric means, as well as the new method of minimax log-Chebyshev approximation, for which the solution is obtained using the apparatus and methods of tropical (idempotent) mathematics. Comparison of the solutions obtained shows that the use of different methods does not always lead to the same or close results. If the results of different methods differ significantly the choice of one of them for making a decision does not seem entirely justified. On the contrary, the coincidence or similarity of these results can be considered as some additional argument in favor of choosing one of them as a solution close to the optimum.