Annals of Operations Research

, Volume 274, Issue 1–2, pp 57–74

# Deriving priorities from inconsistent PCM using network algorithms

• Marcin Anholcer
• 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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