Deriving Priorities From Inconsistent PCM using the Network Algorithms

TL;DR

This paper addresses the challenge of approximating inconsistent Pairwise Comparison Matrices in multiobjective decision-making by formulating the problem as a shortest path problem, enabling efficient solutions with unique, Pareto-efficient outcomes.

Contribution

It introduces a novel approach to minimize the maximum distance in PCM approximation using network algorithms, providing a complete characterization of optimal solutions.

Findings

Formulation of PCM inconsistency minimization as a shortest path problem.

Development of an efficient algorithm for unique Pareto-efficient solutions.

Complete characterization of the set of optimal solutions.

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.