An LP-based inconsistency monitoring of pairwise comparison matrices

TL;DR

This paper introduces a linear programming approach to monitor inconsistency in pairwise comparison matrices, enabling real-time feedback during matrix completion and detecting errors early.

Contribution

It extends a distance-based inconsistency indicator to incomplete matrices and transforms the problem into a linear programming model for practical application.

Findings

The method detects high inconsistency during matrix filling.

It provides automatic feedback to prevent errors.

Numerical examples demonstrate effectiveness.

Abstract

A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent linear programming problem. The results can be applied in the process of filling in the matrix as the decision maker gets automatic feedback. As soon as a serious error occurs among the matrix elements, even due to a misprint, a significant increase in the inconsistency index is reported. The high inconsistency may be alarmed not only at the end of the process of filling in the matrix but also during the completion process. Numerical examples are also provided.