Academy
This page is published in English.
Consistency
Koczkodaj Inconsistency Index - Triad-based pairwise consistency measure
Pairwise consistency index - triad-based
Koczkodaj, W.W.1993doi:10.1016/0895-7177(93)90059-8 ↗
Overview
Koczkodaj K < 0.1 is acceptable. K identifies the single worst triad - ask the DM to revise those specific entries.
- Output
- Consistency Score, lower is better
- Data
- Crisp, positive reciprocal
- Size
- 3+ alternatives, 3-9 criteria works best
- Used for
- Multi-criteria decision making, AHP, pairwise comparison
Fits when / Look elsewhere when
Fits when
- •Identifies exact worst triad
- •Does not require eigenvalue computation
- •Scale-invariant
Look elsewhere when
- •Aggregated group PCMs are used (CI/CR more standard in practice)
Assumptions to verify
- PCM entries are positive and reciprocal
Limitations
- •Only flags worst triad; overall distribution not visible from K alone
Edge cases and pitfalls
Confusing K with Saaty CR: K is max-based (worst triad), CR is average-based. K < 0.1 and CR < 0.1 are different thresholds.
For n>3, many triads exist; K only flags the worst - inspect the full triad table.
Works with
How to cite
Koczkodaj, W.W. (1993). A new definition of consistency of pairwise comparisons. Mathematical and Computer Modelling. https://doi.org/10.1016/0895-7177(93)90059-8
System ID, as it appears in reports and the API
CONSISTENCY-KOCZKODAJ