TY - CHAP

T1 - Tropical optimization techniques in multi-criteria decision making with Analytical Hierarchy Process

AU - Кривулин, Николай Кимович

AU - Sergeev, Sergei

N1 - Conference code: 11

PY - 2017

Y1 - 2017

N2 - 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. The framework involves the Chebyshev approximation of pairwise comparison matrices by consistent matrices in the logarithmic scale. We reduce the log-Chebyshev approximation to multidimensional tropical optimization problems, and offer complete direct solutions to the problems in the framework of tropical mathematics. The results obtained provide a closed-form solution to the rating problem of interest as either a unique score vector (up to a positive factor) or as a set of different score vectors. To handle the problem when the solution is not unique, we develop tropical optimization techniques 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 can be well representative of the entire solution.

AB - 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. The framework involves the Chebyshev approximation of pairwise comparison matrices by consistent matrices in the logarithmic scale. We reduce the log-Chebyshev approximation to multidimensional tropical optimization problems, and offer complete direct solutions to the problems in the framework of tropical mathematics. The results obtained provide a closed-form solution to the rating problem of interest as either a unique score vector (up to a positive factor) or as a set of different score vectors. To handle the problem when the solution is not unique, we develop tropical optimization techniques 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 can be well representative of the entire solution.

KW - tropical mathematics

KW - max-algebra

KW - tropical optimization problem

KW - pairwise comparison

KW - log-Chebyshev approximation

KW - multi-criteria decision

KW - Analytical Hierarchy Process

UR - https://arxiv.org/abs/1801.10524

U2 - 10.1109/EMS.2017.18

DO - 10.1109/EMS.2017.18

M3 - Chapter

SN - 978-1-5386-1411-2

T3 - European Modelling Symposium (EMS)

SP - 38

EP - 43

BT - 2017 European Modelling Symposium (EMS)

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - UKSim-AMSS 11th European Modelling Symposium on Mathematical Modelling and Computer Simulation<br/>

Y2 - 20 November 2017 through 22 November 2017

ER -