Methods of tropical optimization in rating alternatives based on pairwise comparisons
Provides a new mathematical framework for multi-criteria decision-making problems where pairwise comparisons are used, offering explicit solutions and analysis of solution sets.
The paper applies tropical optimization to solve the log-Chebyshev approximation problem for pairwise comparison matrices, deriving closed-form solutions and analyzing non-unique cases to find score vectors that minimize or maximize differentiation between alternatives.
We apply methods of tropical optimization to handle problems of rating alternatives on the basis of the log-Chebyshev approximation of pairwise comparison matrices. We derive a direct solution in a closed form, and investigate the obtained solution when it is not unique. Provided the approximation problem yields a set of score vectors, rather than a unique (up to a constant factor) one, we find those vectors in the set, which least and most differentiate between the alternatives with the highest and lowest scores, and thus can be representative of the entire solution.