ROC: Rank Order Centroid weights (rank-based surrogate weights)

Overview

Weight_Subjective. Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Weight_Subjective
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

• •Assumes: Domain experts available
• •Assumes: Experts can express consistent comparisons

Assumptions to verify

• •Domain experts available
• •Experts can express consistent comparisons

When not to use

• •No experts available → use objective weighting
• •High inconsistency → discard and re-elicit

Edge cases

• •See F.steps and D.parameters for ROC-WEIGHT-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'ROC-WEIGHT bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Domain experts available
• •Hatalı: 'ROC-WEIGHT bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Experts can express consistent comparisons
• •Hatalı: ROC-WEIGHT'yi 'No experts available → use objective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: ROC-WEIGHT'yi 'High inconsistency → discard and re-elicit' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): ROC weight for the criterion with rank r (out of n): w_r = (1/n) Σ_{k=r}^{n} (1/k). This is the centroid of the simplex constrained by the rank ordering. Formül: w_r = \frac{1}{n}\sum_{k=r}^{n}\frac{1}{k},\quad r=1,\ldots,n Anchor: Barron & Barrett 1996, p.1517 Eq.(2) (pending PDF page verification)

Commonly paired with

• •ROC-WEIGHT + TOPSIS (high)
• •ROC-WEIGHT + VIKOR (high)
• •ROC-WEIGHT + EDAS (high)
• •ROC-WEIGHT + PROMETHEE (high)
• •ROC-WEIGHT + ELECTRE-III (high)

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