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Deriving priorities from inconsistent PCM using network algorithms

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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.

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Correspondence to Marcin Anholcer .

Additional information

The research of the first author was part of the project financed by the National Science Center grant awarded on the basis of the Decision Number DEC-2011/01/D/HS4/03543. The research of the second author was supported in part by OTKA Grant 111797.

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Anholcer , M., Fülöp, J. Deriving priorities from inconsistent PCM using network algorithms. Ann Oper Res 274, 57–74 (2019). https://doi.org/10.1007/s10479-018-2888-x

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