Axiomatization of inconsistency indicators for pairwise comparisons

This study proposes revised axioms for defining inconsistency indicators in pairwise comparisons. It includes 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 giv...

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Bibliographic Details
Published in:International journal of approximate reasoning 2018-03, Vol.94, p.18-29
Main Authors: Koczkodaj, W.W., Urban, R.
Format: Article
Language:English
Subjects:
Axiom
Exponentially invertible measure
Inconsistency
Normalization
Pairwise comparison
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Summary:This study proposes revised axioms for defining inconsistency indicators in pairwise comparisons. It includes 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. The use of normalized distance for the inconsistency at the level of a triad corrected the former insufficiency in expressing it in the 2014 study on axiomatization by Koczkodaj and Szwarc. •The proposed axiomatization of inconsistency indicators prevent error aberations taking place in the past.•A new innovative exponentially invertible measure (EIM) is introduced for expressing some axioms.•Mathematical evidence was provided that the popular eigenvalue-based Consistency Index (CI), is incorrect.•CI is one of the pillars of Analytical Hierarchy Process (also known as AHP) but no longer valid.•Reasoning for normalization of inconsistency indicators is provided and postulated.
ISSN:0888-613X
1873-4731
DOI:10.1016/j.ijar.2017.12.001