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Deriving priorities from inconsistent PCM using network algorithms

Author

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  • Marcin Anholcer

    (Poznań University of Economics and Business)

  • János Fülöp

    (Hungarian Academy of Sciences)

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.

Suggested Citation

  • Marcin Anholcer & János Fülöp, 2019. "Deriving priorities from inconsistent PCM using network algorithms," Annals of Operations Research, Springer, vol. 274(1), pages 57-74, March.
    • Handle: RePEc:spr:annopr:v:274:y:2019:i:1:d:10.1007_s10479-018-2888-x
    DOI: 10.1007/s10479-018-2888-x
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    References listed on IDEAS

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    2. Furtado, Susana & Johnson, Charles R., 2024. "Efficiency analysis for the Perron vector of a reciprocal matrix," Applied Mathematics and Computation, Elsevier, vol. 480(C).

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