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September 10, 2025Open Access

Solving multicriteria problems of rating alternatives based on pairwise comparisons

Key Points

The proposed methods effectively address multicriteria problems using pairwise comparisons, improving decision-making processes.
Numerical solutions were derived using various techniques including the analytic hierarchy process and weighted geometric means.
Log-Chebyshev approximation models tropical mathematics concepts, enabling innovations in handling pairwise comparison matrices.
The use of idempotent operations from tropical mathematics offers unique insights into traditional multicriteria evaluation methods.

Abstract

Well-known examples of multicriteria problems of evaluating alternatives based on paired comparisons are considered. Numerical solutions to these problems are presented, obtained using the method of analytic hierarchy process, the method of weighted geometric means, and also a method based on the log-Chebyshev approximation of pairwise comparison matrices. When solving problems using log-Chebyshev approximation, models and methods of tropical mathematics are used, which studies the theory and applications of algebraic systems with idempotent operations.

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