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 -