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Annals of Operations Research

, Volume 274, Issue 1–2, pp 57–74 | Cite as

Deriving priorities from inconsistent PCM using network algorithms

  • Marcin Anholcer Email author
  • János Fülöp
Original Research

Abstract

In several multiobjective decision problems Pairwise Comparison Matrices (PCM) are applied to evaluate the decision variants. The problem that arises very often is the inconsistency of a given PCM. In such a situation it is important to approximate the PCM with a consistent one. One of the approaches is to minimize the distance between the matrices, most often the Euclidean distance. In the paper we consider the problem of minimizing the maximum distance. After applying the logarithmic transformation we are able to formulate the obtained subproblem as a Shortest Path Problem and solve it more efficiently. We analyze the structure of the set of optimal solutions and prove some of its properties. This allows us to provide an iterative algorithm that results in a unique, Pareto-efficient solution.

Keywords

Pairwise comparisons Shortest Path Problem Network Simplex method Pareto efficiency 

Mathematics Subject Classification

90B50 90B10 90C35 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Faculty of Informatics and Electronic EconomyPoznań University of Economics and BusinessPoznańPoland
  2. 2.Research Group of Operations Research and Decision Systems, Institute for Computer Science and ControlHungarian Academy of SciencesBudapestHungary

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