A comparative study on distance-based inconsistency indices defined over Abelian linearly ordered groups

Abstract

Pairwise comparisons have been a long-standing technique for comparing alternatives/criteria and their role has been pivotal in the development of modern decision-making methods. Pairwise comparisons can be performed within several theoretical frameworks such as multiplicative, additive and fuzzy preference systems, which are particular instances of a more general framework based on Abelian linearly ordered groups. Although, in this general algebraic framework, three distance-based inconsistency indices have been proposed, no comparative study has been conducted on them; thus, this paper aims at filling this gap. In particular, we look for relationships and functional relations between these inconsistency indices and whenever a functional relation does not exist, we analyze their correlation and determine the regression curve of an index on another one.