COPRAS: Complex Proportional Assessment

Overview

Proportional assessment (benefit/cost split). Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Proportional assessment (benefit/cost split)

Limitations

• •Rank reversal known on alternative-set changes (ref: general MCDM literature)
• •Assumes: Criteria preferences are independent (no synergistic interactions)
• •Assumes: Compensation is acceptable: high score on one criterion can offset low on another
• •Assumes: Decision matrix is complete (no missing values)

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)

When not to use

• •Criteria strongly correlated → consider DEMATEL/ANP for interdependence
• •Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)

Edge cases

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

Common pitfalls

• •Hatalı: 'COPRAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'COPRAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'COPRAS bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: COPRAS'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: COPRAS'yi 'Non-compensatory preferences → consider outranking (ELECTRE/PROMETHEE)' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Linear sum normalisation r_ij = x_ij / Σ x_kj. Formül: r_{ij} = \dfrac{x_{ij}}{\sum_{k=1}^{m} x_{kj}} Anchor: Zavadskas-Kaklauskas 1996, Eq.(2)
2. 2.Adım 2 (F2): Step 2: Weighted normalised matrix d_ij = w_j · r_ij. Formül: d_{ij} = w_{j} \cdot r_{ij} Anchor: Zavadskas-Kaklauskas 1996, Eq.(3)
3. 3.Adım 3 (F3): Step 3: Sum benefit S+_i and cost S−_i. Formül: S^{+}_{i} = \sum_{j\in J^{+}} d_{ij},\quad S^{-}_{i} = \sum_{j\in J^{-}} d_{ij} Anchor: Zavadskas-Kaklauskas 1996, Eqs.(4)-(5)
4. 4.Adım 4 (F4): Step 4: Relative significance Q_i (Zavadskas-Kaklauskas compound). Formül: Q_{i} = S^{+}_{i} + \dfrac{\min_{k} S^{-}_{k}\cdot \sum_{k} S^{-}_{k}}{S^{-}_{i}\cdot \sum_{k} \dfrac{\min_{k} S^{-}_{k}}{S^{-}_{k}}} Anchor: Zavadskas-Kaklauskas 1996, Eq.(6)
5. 5.Adım 5 (F5): Step 5: Utility degree N_i (percent of best) and descending ranking. Formül: N_{i} = \dfrac{Q_{i}}{\max_{k} Q_{k}} \times 100\% Anchor: Zavadskas-Kaklauskas 1996, Eq.(7)

Commonly paired with

• •AHP + COPRAS (high)
• •BWM + COPRAS (high)
• •ENTROPY + COPRAS (high)
• •CRITIC + COPRAS (high)
• •SWARA + COPRAS (high)

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