Algebraic solution to box-constrained bi-criteria problem of rating alternatives through pairwise comparisons

We consider a decision-making problem to evaluate absolute ratings of alternatives that are compared in pairs according two criteria, subject box constraints on the ratings. The is formulated as log-Chebyshev approximation pairwise comparison matrices by common consistent matrix (a symmetrically reciprocal unit rank), minimize errors for both simultaneously. rearrange constrained bi-objective optimization finding vector determines approximating matrix, and then represent terms tropical algebra. apply methods results derive an analytical solution problem. consists introducing new variables describe values objective functions allow reducing system parameterized inequalities constructed unknown vector, where play role parameters. exploit existence condition solutions those parameters belong Pareto front inherent Then, we solve take all correspond front, complete result obtained bi-criteria decision under consideration present illustrative examples.