Efficiency analysis of double perturbed pairwise comparison matrices

Abstract

Efficiency is a core concept of multi-objective optimisation problems and multi-attribute decision-making. In the case of pairwise comparison matrices, a weight vector is called efficient if the approximations of the elements of the pairwise comparison matrix made by the ratios of the weights cannot be improved in any position without making it worse in some other position. A pairwise comparison matrix is called double perturbed if it can be made consistent by altering two elements and their reciprocals. The most frequently used weighting method, the eigenvector method is analysed in the paper, and it is shown that it produces an efficient weight vector for double perturbed pairwise comparison matrices.

Keywords:

• Pairwise comparison matrix
• efficiency
• Pareto optimality
• eigenvector

Acknowledgements

The authors are grateful to the anonymous reviewers for their constructive remarks. András Farkas (Óbuda University, Budapest) and János Fülöp (Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI) and Óbuda University, Budapest) are greatly acknowledged for their valuable comments. S. Bozóki acknowledges the support of the János Bolyai Research Fellowship no. BO/00154/16/3.

Notes

No potential conflict of interest was reported by the authors.

Supplemental data for this article can be accessed at https://doi.org/10.1080/01605682.2017.1409408.

1 Note there is a misprint in the cited table, the number in the “3 elements to modify” column in the $4\times 4$ row should be 6 instead of 0)