CRITIC: CRiteria Importance Through Intercriteria Correlation

Overview

Statistical contrast intensity + correlation-based objective weighting. Output typically weight (higher value = preferred).

Strengths

• •Method-specific: Statistical contrast intensity + correlation-based objective weighting

Limitations

• •Assumes: Decision matrix exists with measurable criteria
• •Assumes: Sufficient inter-alternative variation per criterion

Assumptions to verify

• •Decision matrix exists with measurable criteria
• •Sufficient inter-alternative variation per criterion

When not to use

• •No data variation (constant criterion) → weight degenerates
• •Expert judgment is the actual driver → use subjective weighting

Edge cases

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

Common pitfalls

• •Hatalı: 'CRITIC bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix exists with measurable criteria
• •Hatalı: 'CRITIC bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Sufficient inter-alternative variation per criterion
• •Hatalı: CRITIC'yi 'No data variation (constant criterion) → weight degenerates' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: CRITIC'yi 'Expert judgment is the actual driver → use subjective weighting' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): Step 1: Min-max normalisation per criterion direction. Benefit: (x−min)/(max−min); cost: (max−x)/(max−min). Result x̄_ij ∈ [0,1]. Formül: \bar{x}_{ij} = \dfrac{x_{ij}-\min_{i} x_{ij}}{\max_{i} x_{ij}-\min_{i} x_{ij}}\ (J^{+});\quad \dfrac{\max_{i} x_{ij}-x_{ij}}{\max_{i} x_{ij}-\min_{i} x_{ij}}\ (J^{-}) Anchor: Diakoulaki 1995, p.765 Eq.(1)
2. 2.Adım 2 (F2): Step 2: Standard deviation σ_j per criterion (population variant, divide by m). Relative weights are identical with sample std (divide by m-1) because σ enters uniformly across criteria. Formül: \sigma_{j} = \sqrt{\dfrac{1}{m} \sum_{i=1}^{m} (\bar{x}_{ij}-\bar{\bar{x}}_{j})^{2}},\quad \bar{\bar{x}}_{j} = \frac{1}{m}\sum_{i} \bar{x}_{ij} Anchor: Diakoulaki 1995, p.766 Eq.(2)
3. 3.Adım 3 (F3): Step 3: Pearson correlation ρ_jk between every criterion pair, computed on the normalised matrix N (NOT the raw X). Formül: \rho_{jk} = \dfrac{\sum_{i}(\bar{x}_{ij}-\bar{\bar{x}}_{j})(\bar{x}_{ik}-\bar{\bar{x}}_{k})}{\sqrt{\sum_{i}(\bar{x}_{ij}-\bar{\bar{x}}_{j})^{2} \sum_{i}(\bar{x}_{ik}-\bar{\bar{x}}_{k})^{2}}} Anchor: Diakoulaki 1995, p.766 Eq.(3)
4. 4.Adım 4 (F4): Step 4: Information amount C_j = σ_j · Σ_k (1−ρ_jk). High contrast (σ_j large) AND low correlation with other criteria (Σ(1-ρ) large) yields higher C_j. Formül: C_{j} = \sigma_{j} \sum_{k=1}^{n} (1 - \rho_{jk}) Anchor: Diakoulaki 1995, p.766 Eq.(4)
5. 5.Adım 5 (F5): Step 5: Normalised CRITIC weights w_j = C_j / Σ_k C_k; Σ w_j = 1. Formül: w_{j} = \dfrac{C_{j}}{\sum_{k=1}^{n} C_{k}},\quad \sum_{j=1}^{n} w_{j} = 1 Anchor: Diakoulaki 1995, p.766 Eq.(5)

Commonly paired with

• •CRITIC + TOPSIS (high)
• •CRITIC + VIKOR (high)
• •CRITIC + EDAS (high)
• •CRITIC + WASPAS (high)
• •CRITIC + MARCOS (high)

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