Axiomatization of Inconsistency Indicators for Pairwise Comparisons

Abstract

This study proposes revised axioms for defining inconsistency indicators in pairwise comparisons. It is based on the new findings that "PC submatrix cannot have a worse inconsistency indicator than the PC matrix containing it" and that there must be a PC submatrix with the same inconsistency as the given PC matrix. This study also provides better reasoning for the need of normalization. It is a revision of axiomatization by Koczkodaj and Szwarc, 2014 which proposed axioms expressed informally with some deficiencies addressed in this study.Comment: This paper should have been withdrawn by the first author a long time ago. The work has been finished with another researcher, I have been pushed out the projec