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Abstract
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.
Original language | English |
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Pages (from-to) | 31-51 |
Number of pages | 21 |
Journal | Fuzzy Sets and Systems |
Volume | 377 |
Early online date | 29 Oct 2018 |
DOIs | |
Publication status | Published - 15 Dec 2019 |
Keywords
- Tropical optimization
- Max-algebra
- Pairwise comparison
- Log-Chebyshev approximation
- Analytic Hierarchy Process
- Hilbert distance
ASJC Scopus subject areas
- General Mathematics
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Dive into the research topics of 'Tropical implementation of the Analytical Hierarchy Process decision method'. Together they form a unique fingerprint.Projects
- 1 Finished
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Tropical Optimisation
Sergeev, S. (Principal Investigator)
Engineering & Physical Science Research Council
1/04/17 → 31/08/19
Project: Research Councils