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Tropical optimization techniques for solving multicriteria problems in decision making. / Кривулин, Николай Кимович.

International Conference Polynomial Computer Algebra ‘2022 (PCA 2022): International Conference Polynomial Computer Algebra '2022. St. Petersburg, May 2-7, 2022. Euler International Mathematical Institute. ред. / N. N. Vassiliev. Санкт-Петербург : Издательство «ВВМ», 2022. стр. 46-52.

Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференцииРецензирование

Harvard

Кривулин, НК 2022, Tropical optimization techniques for solving multicriteria problems in decision making. в NN Vassiliev (ред.), International Conference Polynomial Computer Algebra ‘2022 (PCA 2022): International Conference Polynomial Computer Algebra '2022. St. Petersburg, May 2-7, 2022. Euler International Mathematical Institute. Издательство «ВВМ», Санкт-Петербург, стр. 46-52, Polynomial Computer Algebra 2022, Санкт-Петербург, Российская Федерация, 2/05/22. https://doi.org/https://www.elibrary.ru/item.asp?id=48599449

APA

Кривулин, Н. К. (2022). Tropical optimization techniques for solving multicriteria problems in decision making. в N. N. Vassiliev (Ред.), International Conference Polynomial Computer Algebra ‘2022 (PCA 2022): International Conference Polynomial Computer Algebra '2022. St. Petersburg, May 2-7, 2022. Euler International Mathematical Institute (стр. 46-52). Издательство «ВВМ». https://doi.org/https://www.elibrary.ru/item.asp?id=48599449

Vancouver

Кривулин НК. Tropical optimization techniques for solving multicriteria problems in decision making. в Vassiliev NN, Редактор, International Conference Polynomial Computer Algebra ‘2022 (PCA 2022): International Conference Polynomial Computer Algebra '2022. St. Petersburg, May 2-7, 2022. Euler International Mathematical Institute. Санкт-Петербург: Издательство «ВВМ». 2022. стр. 46-52 https://doi.org/https://www.elibrary.ru/item.asp?id=48599449

Author

Кривулин, Николай Кимович. / Tropical optimization techniques for solving multicriteria problems in decision making. International Conference Polynomial Computer Algebra ‘2022 (PCA 2022): International Conference Polynomial Computer Algebra '2022. St. Petersburg, May 2-7, 2022. Euler International Mathematical Institute. Редактор / N. N. Vassiliev. Санкт-Петербург : Издательство «ВВМ», 2022. стр. 46-52

BibTeX

@inproceedings{88eb2edda94d425da958f300e8ed902b,
title = "Tropical optimization techniques for solving multicriteria problems in decision making",
abstract = "We consider a decision-making problem to find ratings of alternatives from pairwise comparisons under several criteria, subject to constraints imposed on the ratings. Given matrices of pairwise comparisons, the problem is formulated as the log-Chebyshev approximation of these matrices by a common consistent matrix (a symmetrically reciprocal matrix of unit rank) that minimizes the approximation errors for all matrices simultaneously. We rearrange the approximation problem as a constrained multiobjective optimization problem of finding a vector that determines the approximating matrix. The optimization problem is then represented in the framework of tropical algebra. We apply methods and results of tropical optimization to solve the problem according to various principles of optimality, including the max-ordering, lexicographic ordering and lexicographic max-ordering optimality.",
author = "Кривулин, {Николай Кимович}",
note = "Krivulin N. Tropical optimization techniques for solving multicriteria problems in decision making // International Conference Polynomial Computer Algebra '2022. St. Petersburg, May 2-7, 2022. Euler International Mathematical Institute. Ed. by N.N. Vassiliev. St. Petersburg, VVM Publishing, 2022. P.46-52.; null ; Conference date: 02-05-2022 Through 07-05-2022",
year = "2022",
doi = "https://www.elibrary.ru/item.asp?id=48599449",
language = "English",
isbn = "978-5-9651-1425-2",
pages = "46--52",
editor = "Vassiliev, {N. N.}",
booktitle = "International Conference Polynomial Computer Algebra {\textquoteleft}2022 (PCA 2022)",
publisher = "Издательство «ВВМ»",
address = "Russian Federation",
url = "https://pca-pdmi.ru/2022/program",

}

RIS

TY - GEN

T1 - Tropical optimization techniques for solving multicriteria problems in decision making

AU - Кривулин, Николай Кимович

N1 - Krivulin N. Tropical optimization techniques for solving multicriteria problems in decision making // International Conference Polynomial Computer Algebra '2022. St. Petersburg, May 2-7, 2022. Euler International Mathematical Institute. Ed. by N.N. Vassiliev. St. Petersburg, VVM Publishing, 2022. P.46-52.

PY - 2022

Y1 - 2022

N2 - We consider a decision-making problem to find ratings of alternatives from pairwise comparisons under several criteria, subject to constraints imposed on the ratings. Given matrices of pairwise comparisons, the problem is formulated as the log-Chebyshev approximation of these matrices by a common consistent matrix (a symmetrically reciprocal matrix of unit rank) that minimizes the approximation errors for all matrices simultaneously. We rearrange the approximation problem as a constrained multiobjective optimization problem of finding a vector that determines the approximating matrix. The optimization problem is then represented in the framework of tropical algebra. We apply methods and results of tropical optimization to solve the problem according to various principles of optimality, including the max-ordering, lexicographic ordering and lexicographic max-ordering optimality.

AB - We consider a decision-making problem to find ratings of alternatives from pairwise comparisons under several criteria, subject to constraints imposed on the ratings. Given matrices of pairwise comparisons, the problem is formulated as the log-Chebyshev approximation of these matrices by a common consistent matrix (a symmetrically reciprocal matrix of unit rank) that minimizes the approximation errors for all matrices simultaneously. We rearrange the approximation problem as a constrained multiobjective optimization problem of finding a vector that determines the approximating matrix. The optimization problem is then represented in the framework of tropical algebra. We apply methods and results of tropical optimization to solve the problem according to various principles of optimality, including the max-ordering, lexicographic ordering and lexicographic max-ordering optimality.

U2 - https://www.elibrary.ru/item.asp?id=48599449

DO - https://www.elibrary.ru/item.asp?id=48599449

M3 - Conference contribution

SN - 978-5-9651-1425-2

SP - 46

EP - 52

BT - International Conference Polynomial Computer Algebra ‘2022 (PCA 2022)

A2 - Vassiliev, N. N.

PB - Издательство «ВВМ»

CY - Санкт-Петербург

Y2 - 2 May 2022 through 7 May 2022

ER -

ID: 96211498