### Abstract

Original language | English |
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Publication status | Published - May 2018 |

Event | XV International Conference on Computational Management Science - Norwegian University of Science and Technology (NTNU), Trondheim Duration: 29 May 2018 → 31 May 2018 https://www.ntnu.edu/cms2018 |

### Conference

Conference | XV International Conference on Computational Management Science |
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Abbreviated title | CMS 2018 |

Country | Norway |

City | Trondheim |

Period | 29/05/18 → 31/05/18 |

Internet address |

### Fingerprint

### Scopus subject areas

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

### Cite this

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

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

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 -