Activities per year
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 logChebyshev 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 language  English 

Title of host publication  2016 Proceedings of the Seventh SIAM Workshop on Combinatorial Scientific Computing 
Editors  Assefaw H. Gebremedhin, Erik G. Boman, Bora Ucar 
Publisher  Society for Industrial and Applied Mathematics 
Pages  6272 
Number of pages  11 
ISBN (Electronic)  9781611974690 
DOIs  
State  Published  2016 
Event  The Seventh SIAM Workshop on Combinatorial Scientific Computing  Albuquerque, United States Duration: 10 Oct 2016 → 12 Oct 2016 Conference number: 7 https://archive.siam.org/meetings/csc16/csc16.html 
Publication series
Name  Proceedings 

Publisher  Society for Industrial and Applied Mathematics 
Conference
Conference  The Seventh SIAM Workshop on Combinatorial Scientific Computing 

Abbreviated title  CSC 2016 
Country  United States 
City  Albuquerque 
Period  10/10/16 → 12/10/16 
Internet address 
Scopus subject areas
 Decision Sciences (miscellaneous)
 Computational Mathematics
 Algebra and Number Theory
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Activities

Using tropical optimization techniques to evaluate alternatives via pairwise comparisons
Николай Кимович Кривулин (Speaker)
10 Oct 2016Activity: Talk types › Oral presentation

The Seventh SIAM Workshop on Combinatorial Scientific Computing
Николай Кимович Кривулин (Participant)
10 Oct 2016 → 12 Oct 2016Activity: Attendance types › Participating in a conference, workshop, ...