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Ranking
COBRA - COmprehensive distance Based RAnking
Distance from PIS/NIS/AS (Euclidean base plus scaled Euclidean-Taxicab interaction)
Krstić, M., Agnusdei, G. P., Tadić, S., Kovač, M., Miglietta, P. P.2022doi:10.3390/su14095632 ↗
Overview
dC_i can be any real number. Lower dC means the alternative is closer to PIS and AS+, and farther from NIS and AS-. Rank 1 (best) is the alternative with the smallest dC.
- Output
- distance score, lower is better
- Data
- Crisp, complete numeric matrix
- Weights
- Needs a weight source
- Size
- 2+ alternatives, 3-12 criteria works best
- Used for
- Alternative selection, Supplier evaluation, sustainable performance assessment
Fits when / Look elsewhere when
Fits when
- •Combines both Euclidean and Taxicab distance metrics
- •Uses PIS, NIS and average solution as reference points simultaneously
- •Direction-agnostic normalisation avoids bias from criterion direction
Assumptions to verify
- Criteria preferences are independent (no synergistic interactions)
- Compensation is acceptable: high score on one criterion can offset low on another
- Decision matrix is complete (no missing values)
Limitations
- •Assumes criteria preferences are independent (no synergistic interactions)
- •Assumes compensation is acceptable
- •Assumes decision matrix is complete (no missing values)
Edge cases and pitfalls
COBRA normalisation is direction-agnostic (always divide by max); direction is only applied when computing PIS/NIS in F4. Do not apply direction-based normalisation at F2.
AS+ uses ONLY criteria where Δw_ij > AS_j (strictly above); AS- uses ONLY criteria where Δw_ij < AS_j (strictly below). Components equal to AS contribute zero.
σ in the combined distance is recomputed independently for each reference point (PIS, NIS, AS+, AS-).
Works with
How to cite
Krstić, M.; Agnusdei, G. P.; Tadić, S.; Kovač, M.; Miglietta, P. P. (2022). A Novel Axiomatic DEA-COBRA Framework for Evaluating the Sustainable Performance of Agri-Food Systems. Sustainability. https://doi.org/10.3390/su14095632
System ID, as it appears in reports and the API
COBRA