Comparative study of inconsistency indices based on a notion of a triad inconsistency

Abstract

Many prioritization methods are based on a pairwise comparison matrix (PCM). In the applications of the PCM, a special attention is paid to the PCM inconsistency analysis. To characterize this inconsistency some indices are proposed. All inconsistency indices proposed in literature share two features: they are nonnegative and equal 0 if and only if a given PCM is consistent. From purely mathematical point of view we have infinitely many nonnegative matrix functions that satisfy such conditions. In this paper we propose a new class of inconsistency indices that is based on a notion of a triad inconsistency. Their performance is compared with the help of Monte Carlo experiments. In these experiments the criterion for the indices performance is their relationship with the final-priority-estimates-errors.