TY - CHAP

T1 - Using tropical optimization techniques to evaluate alternatives via pairwise comparisons

AU - Кривулин, Николай Кимович

N1 - Conference code: 7

PY - 2016

Y1 - 2016

N2 - We describe a new approach based on tropical optimization techniques to solve the problem of rating alternatives from pairwise comparison data. The problem is formulated to approximate, in the log-Chebyshev sense, pairwise comparison matrices by reciprocal matrices of unit rank, and then represented in general terms of tropical mathematics as a tropical optimization problem. The optimization problem takes a common, unified form for both multiplicative and additive comparison scales. We apply recent results in tropical optimization to offer new complete solutions to the rating problems under various assumptions about the pairwise comparison matrices. The solutions are given in a compact vector form, which extends known solutions and involves modest computational efforts. The results obtained are illustrated with numerical examples. Specifically, we show by example that the partial solution known before may miss better results provided by the new complete solution. An example to demonstrate a tropical analogue of the analytical hierarchy process decision scheme is also given.

AB - We describe a new approach based on tropical optimization techniques to solve the problem of rating alternatives from pairwise comparison data. The problem is formulated to approximate, in the log-Chebyshev sense, pairwise comparison matrices by reciprocal matrices of unit rank, and then represented in general terms of tropical mathematics as a tropical optimization problem. The optimization problem takes a common, unified form for both multiplicative and additive comparison scales. We apply recent results in tropical optimization to offer new complete solutions to the rating problems under various assumptions about the pairwise comparison matrices. The solutions are given in a compact vector form, which extends known solutions and involves modest computational efforts. The results obtained are illustrated with numerical examples. Specifically, we show by example that the partial solution known before may miss better results provided by the new complete solution. An example to demonstrate a tropical analogue of the analytical hierarchy process decision scheme is also given.

U2 - 10.1137/1.9781611974690.ch7

DO - 10.1137/1.9781611974690.ch7

M3 - Chapter

T3 - Proceedings

SP - 62

EP - 72

BT - 2016 Proceedings of the Seventh SIAM Workshop on Combinatorial Scientific Computing

A2 - Gebremedhin, Assefaw H.

A2 - Boman, Erik G.

A2 - Ucar, Bora

PB - Society for Industrial and Applied Mathematics

T2 - The Seventh SIAM Workshop on Combinatorial Scientific Computing

Y2 - 10 October 2016 through 12 October 2016

ER -