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We apply methods of tropical optimization to handle problems of ratingalternatives on the basis of the log-Chebyshev approximation of pairwisecomparison matrices. We derive a direct solution in a closed form, andinvestigate the obtained solution when it is not unique. Provided theapproximation problem yields a set of score vectors, rather than a unique (upto a constant factor) one, we find those vectors in the set, which least andmost differentiate between the alternatives with the highest and lowest scores,and thus can be representative of the entire solution.

Methods of tropical optimization in rating alternatives based on pairwise comparisons