Tropical implementation of the Analytical Hierarchy Process decision method

Nikolai Krivulin, Sergeĭ Sergeev

Результат исследований: Научные публикации в периодических изданияхстатья

2 Цитирования (Scopus)

Аннотация

We apply methods and techniques of tropical optimization to develop a new theoretical and computational framework for the implementation of the Analytic Hierarchy Process in multi-criteria problems of rating alternatives from pairwise comparison data. In this framework, we first consider the minimax Chebyshev approximation of pairwise comparison matrices by consistent matrices in the logarithmic scale. Recasting this approximation problem as a problem of tropical pseudo-quadratic programming, we then write out a closed-form solution to it. This solution might be either a unique score vector (up to a positive factor) or a set of different score vectors. To handle the problem when the solution is not unique, we develop tropical optimization techniques of maximizing and minimizing the Hilbert seminorm to find those vectors from the solution set that are the most and least differentiating between the alternatives with the highest and lowest scores, and thus are well representative of the entire solution set.
Язык оригиналаанглийский
Страницы (с-по)31-51
ЖурналFuzzy Sets and Systems
Том377
Ранняя дата в режиме онлайн29 окт 2018
DOI
СостояниеОпубликовано - 15 дек 2019
СобытиеUKSim-AMSS 11th European Modelling Symposium on Mathematical Modelling and Computer Simulation
- Manchester Conference Centre, Manchester, Великобритания
Продолжительность: 20 ноя 201722 ноя 2017
Номер конференции: 11
http://uksim.info/ems2017/ems2017.htm

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Предметные области Scopus

  • Теория оптимизации
  • Теория принятия решений (разное)
  • Алгебра и теория чисел
  • Теория управления и исследование операций
  • Искусственный интеллект
  • Логика

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