Using tropical optimization techniques in multi-criteria decision problems

Research output

2 Downloads (Pure)

Abstract

We consider problems of rating alternatives based on their pairwise comparisons according to several criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall priorities of each alternative. We offer a solution that involve the minimax approximation of the comparison matrices by a common (consistent) matrix of unit rank in terms of the Chebyshev metric in logarithmic scale. The approximation problem reduces to a multi-objective optimization problem to minimize simultaneously the approximation errors for all comparison matrices. We formulate the problem in terms of tropical (idempotent) mathematics, which focuses on the theory and applications of algebraic systems with idempotent addition. To solve the optimization problem obtained, we apply methods and results of tropical optimization to derive a Pareto optimal solution. As an illustration of the approach, we present a complete Pareto optimal solution for a general problem of rating alternatives in the case of two criteria used for comparisons.
Original languageEnglish
Publication statusPublished - May 2018
EventXV International Conference on Computational Management Science - Norwegian University of Science and Technology (NTNU), Trondheim
Duration: 29 May 201831 May 2018
https://www.ntnu.edu/cms2018

Conference

ConferenceXV International Conference on Computational Management Science
Abbreviated titleCMS 2018
CountryNorway
CityTrondheim
Period29/05/1831/05/18
Internet address

Fingerprint

Multi-criteria
Decision problem
Optimization Techniques
Pareto Optimal Solution
Pairwise Comparisons
Idempotent
Alternatives
Approximation Problem
Multiobjective Optimization Problems
Approximation Error
Chebyshev
Minimax
Logarithmic
Optimization Problem
Minimise
Metric
Unit
Optimization techniques
Multi-criteria decision
Optimization

Scopus subject areas

  • Management Science and Operations Research
  • Control and Optimization
  • Algebra and Number Theory

Cite this

Кривулин, Н. К. (2018). Using tropical optimization techniques in multi-criteria decision problems. Abstract from XV International Conference on Computational Management Science, Trondheim, .
Кривулин, Николай Кимович. / Using tropical optimization techniques in multi-criteria decision problems. Abstract from XV International Conference on Computational Management Science, Trondheim, .
@conference{adedd7cabc614954ae1300c392c671b7,
title = "Using tropical optimization techniques in multi-criteria decision problems",
abstract = "We consider problems of rating alternatives based on their pairwise comparisons according to several criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall priorities of each alternative. We offer a solution that involve the minimax approximation of the comparison matrices by a common (consistent) matrix of unit rank in terms of the Chebyshev metric in logarithmic scale. The approximation problem reduces to a multi-objective optimization problem to minimize simultaneously the approximation errors for all comparison matrices. We formulate the problem in terms of tropical (idempotent) mathematics, which focuses on the theory and applications of algebraic systems with idempotent addition. To solve the optimization problem obtained, we apply methods and results of tropical optimization to derive a Pareto optimal solution. As an illustration of the approach, we present a complete Pareto optimal solution for a general problem of rating alternatives in the case of two criteria used for comparisons.",
author = "Кривулин, {Николай Кимович}",
year = "2018",
month = "5",
language = "English",
note = "XV International Conference on Computational Management Science, CMS 2018 ; Conference date: 29-05-2018 Through 31-05-2018",
url = "https://www.ntnu.edu/cms2018",

}

Using tropical optimization techniques in multi-criteria decision problems. / Кривулин, Николай Кимович.

2018. Abstract from XV International Conference on Computational Management Science, Trondheim, .

Research output

TY - CONF

T1 - Using tropical optimization techniques in multi-criteria decision problems

AU - Кривулин, Николай Кимович

PY - 2018/5

Y1 - 2018/5

N2 - We consider problems of rating alternatives based on their pairwise comparisons according to several criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall priorities of each alternative. We offer a solution that involve the minimax approximation of the comparison matrices by a common (consistent) matrix of unit rank in terms of the Chebyshev metric in logarithmic scale. The approximation problem reduces to a multi-objective optimization problem to minimize simultaneously the approximation errors for all comparison matrices. We formulate the problem in terms of tropical (idempotent) mathematics, which focuses on the theory and applications of algebraic systems with idempotent addition. To solve the optimization problem obtained, we apply methods and results of tropical optimization to derive a Pareto optimal solution. As an illustration of the approach, we present a complete Pareto optimal solution for a general problem of rating alternatives in the case of two criteria used for comparisons.

AB - We consider problems of rating alternatives based on their pairwise comparisons according to several criteria. Given pairwise comparison matrices for each criterion, the problem is to find the overall priorities of each alternative. We offer a solution that involve the minimax approximation of the comparison matrices by a common (consistent) matrix of unit rank in terms of the Chebyshev metric in logarithmic scale. The approximation problem reduces to a multi-objective optimization problem to minimize simultaneously the approximation errors for all comparison matrices. We formulate the problem in terms of tropical (idempotent) mathematics, which focuses on the theory and applications of algebraic systems with idempotent addition. To solve the optimization problem obtained, we apply methods and results of tropical optimization to derive a Pareto optimal solution. As an illustration of the approach, we present a complete Pareto optimal solution for a general problem of rating alternatives in the case of two criteria used for comparisons.

M3 - Abstract

ER -

Кривулин НК. Using tropical optimization techniques in multi-criteria decision problems. 2018. Abstract from XV International Conference on Computational Management Science, Trondheim, .