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Deriving Priorities From Inconsistent PCM using the Network Algorithms

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  • Marcin Anholcer
  • Janos Fulop

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. The most common way is to minimize the Euclidean distance between the matrices. 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 and completely characterize the form of the set of optimal solutions and provide an algorithm that results in a unique, Pareto-efficient solution.

Suggested Citation

  • Marcin Anholcer & Janos Fulop, 2015. "Deriving Priorities From Inconsistent PCM using the Network Algorithms," Papers 1510.04315, arXiv.org.
    • Handle: RePEc:arx:papers:1510.04315
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    References listed on IDEAS

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    1. Lin, Chang-Chun, 2007. "A revised framework for deriving preference values from pairwise comparison matrices," European Journal of Operational Research, Elsevier, vol. 176(2), pages 1145-1150, January.
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    3. R. Blanquero & E. Carrizosa & E. Conde, 2006. "Inferring Efficient Weights from Pairwise Comparison Matrices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(2), pages 271-284, October.
    4. Hovanov, Nikolai V. & Kolari, James W. & Sokolov, Mikhail V., 2008. "Deriving weights from general pairwise comparison matrices," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 205-220, March.
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