A Novel Consistency Index CI-G: Recruiting Compatibility Index G for Consistency Analysis

Claudio Garuti and Enrique Mu ()
Additional contact information
Claudio Garuti: Fulcrum Ingeniería Ltd., Santiago 0180, Chile
Enrique Mu: Department of Business Management, Accounting and Ethics, Carlow University, Pittsburgh, PA 15213, USA

Mathematics, 2025, vol. 13, issue 16, 1-31

Abstract: Consistency indices quantify the degree of transitivity and proportionality violations in a pairwise comparison matrix (PCM), forming a cornerstone of the Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP). Several methods have been proposed to compute consistency, including those based on the maximum eigenvalue, dot product, Jaccard index, and the Bose index. However, these methods often overlook two critical aspects: (i) vector projection or directional alignment, and (ii) the weight or importance of individual elements within a pointwise evaluative structure. The first limitation is particularly impactful. Adjustments made during the consistency improvement process affect the final priority vector disproportionately when heavily weighted elements are involved. Although consistency may improve numerically through such adjustments, the resulting priority vector can deviate significantly, especially when the true vector is known. This indicates that approaches neglecting projection and weighting considerations may yield internally consistent yet externally incompatible vectors, thereby compromising the validity of the analysis. This study builds on the idea that consistency and compatibility are intrinsically related; they are two sides of the same coin and should be considered complementary. To address these limitations, it introduces a novel metric, the Consistency Index G (CI-G) based on the compatibility index G. This measure evaluates how well the columns of a PCM align with its principal eigenvector, using CI-G as a diagnostic component. The proposed approach not only refines consistency measurement but also enhances the accuracy and reliability of derived priorities.

Keywords: analytic hierarchy process; consistency index; consistency index G (CI-G); consistency evaluation; consistency threshold; compatibility index G (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/16/2666/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/16/2666/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:16:p:2666-:d:1727952

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().