Methods of Tropical Optimization in Rating Alternatives Based on Pairwise Comparisons

Conference paper
Part of the Operations Research Proceedings book series (ORP)


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.


Tropical Optimization Alternative Evaluation Pairwise Comparison Matrices Score Vector Represent Optimization Problems 
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This work was supported in part by the Russian Foundation for Humanities (grant No. 16-02-00059). The author is very grateful to the referees for their valuable comments and suggestions, which have been incorporated into the revised version of the manuscript.


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© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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