Using tropical optimization techniques to evaluate alternatives via pairwise comparisons

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Abstract

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.
Original languageEnglish
Title of host publication2016 Proceedings of the Seventh SIAM Workshop on Combinatorial Scientific Computing
EditorsAssefaw H. Gebremedhin, Erik G. Boman, Bora Ucar
PublisherSociety for Industrial and Applied Mathematics
Pages62-72
Number of pages11
ISBN (Electronic)978-1-61197-469-0
DOIs
StatePublished - 2016
EventThe Seventh SIAM Workshop on Combinatorial Scientific Computing - Albuquerque, United States
Duration: 10 Oct 201612 Oct 2016
Conference number: 7
https://archive.siam.org/meetings/csc16/csc16.html

Publication series

NameProceedings
PublisherSociety for Industrial and Applied Mathematics

Conference

ConferenceThe Seventh SIAM Workshop on Combinatorial Scientific Computing
Abbreviated titleCSC 2016
CountryUnited States
CityAlbuquerque
Period10/10/1612/10/16
Internet address

Scopus subject areas

  • Decision Sciences (miscellaneous)
  • Computational Mathematics
  • Algebra and Number Theory

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