# Inconsistency indices for incomplete pairwise comparisons matrices

## TL;DR

This paper adapts twelve inconsistency indices for incomplete pairwise comparison matrices and evaluates their effectiveness through Monte Carlo experiments to improve ranking reliability with incomplete data.

## Contribution

It introduces modifications of existing inconsistency indices to handle incomplete data sets and identifies the most effective ones through experimental validation.

## Key findings

- Modified indices perform well in Monte Carlo tests
- Certain indices are recommended for practical use with incomplete data
- The approach enhances ranking reliability with incomplete comparisons

## Abstract

Comparing alternatives in pairs is a very well known technique of ranking creation. The answer to how reliable and trustworthy ranking is depends on the inconsistency of the data from which it was created. There are many indices used for determining the level of inconsistency among compared alternatives. Unfortunately, most of them assume that the set of comparisons is complete, i.e. every single alternative is compared to each other. This is not true and the ranking must sometimes be made based on incomplete data. In order to fill this gap, this work aims to adapt the selected twelve existing inconsistency indices for the purpose of analyzing incomplete data sets. The modified indices are subjected to Monte Carlo experiments. Those of them that achieved the best results in the experiments carried out are recommended for use in practice.