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Methods of Tropical Optimization in Rating Alternatives Based on Pairwise Comparisons

In: Operations Research Proceedings 2016

Author

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  • Nikolai Krivulin

    (St. Petersburg State University)

Abstract

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.

Suggested Citation

  • Nikolai Krivulin, 2018. "Methods of Tropical Optimization in Rating Alternatives Based on Pairwise Comparisons," Operations Research Proceedings, in: Andreas Fink & Armin Fügenschuh & Martin Josef Geiger (ed.), Operations Research Proceedings 2016, pages 85-91, Springer.
    • Handle: RePEc:spr:oprchp:978-3-319-55702-1_13
    DOI: 10.1007/978-3-319-55702-1_13
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    Cited by:

    1. Nikolai Krivulin, 2020. "Using tropical optimization techniques in bi-criteria decision problems," Computational Management Science, Springer, vol. 17(1), pages 79-104, January.
    2. Nikolai Krivulin & Alexey Prinkov & Igor Gladkikh, 2022. "Using Pairwise Comparisons to Determine Consumer Preferences in Hotel Selection," Mathematics, MDPI, vol. 10(5), pages 1-25, February.

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