Methods of tropical optimization in rating alternatives based on pairwise comparisons

Результат исследований: Материалы конференцийтезисы

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Аннотация

We consider unconstrained and constrained optimization problems in the framework of the tropical (idempotent) mathematics, which focuses on the theory and applications of semirings with idempotent addition. The problems are to minimize or maximize functions defined on vectors over idempotent semifields (semirings with multiplicative inverses). We examine several problems of rating alternatives from pairwise comparisons, including problems with constraints on the final scores of alternatives, and multi-criteria rating problems. We reduce the problems to the log-Chebyshev approximation of pairwise comparison matrices by reciprocal matrices of unit rank, and then represent the approximation problems as optimization problems in the tropical mathematics setting. To solve these problems, methods of tropical optimization are used to provide direct, complete solutions in a compact vector form. We discuss the applicability of the results to real-world problems, and provide numerical examples.
Язык оригиналаанглийский
Страницы38
СостояниеОпубликовано - 2016
СобытиеAnnual International Conference of the German Operations Research Society: International Conference on Operations Research – Analytical Decision Making - Helmut-Schmidt-Universität / Universität der Bundeswehr Hamburg, Hamburg, Германия
Продолжительность: 30 авг 20162 сен 2016
http://or2016.de/

Конференция

КонференцияAnnual International Conference of the German Operations Research Society
Сокращенный заголовокOR 2016
СтранаГермания
ГородHamburg
Период30/08/162/09/16
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Предметные области Scopus

  • Теория принятия решений (разное)
  • Теория оптимизации
  • Алгебра и теория чисел

Цитировать

Кривулин, Н. К. (2016). Methods of tropical optimization in rating alternatives based on pairwise comparisons. 38. Выдержка из Annual International Conference of the German Operations Research Society, Hamburg, Германия.