RAWEC: Ranking Alternatives With Equal Criteria weights

Overview

Rank-based equal-weight aggregation with distance from ideal. Output typically utility (higher value = preferred).

Strengths

• •Method-specific: Rank-based equal-weight aggregation with distance from ideal

Limitations

• •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 RAWEC-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'RAWEC bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Criteria preferences are independent (no synergistic interactions)
• •Hatalı: 'RAWEC bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Compensation is acceptable: high score on one criterion can offset low on another
• •Hatalı: 'RAWEC bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Decision matrix is complete (no missing values)
• •Hatalı: RAWEC'yi 'Criteria strongly correlated → consider DEMATEL/ANP for interdependence' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.
• •Hatalı: RAWEC'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: Construct the initial decision matrix X = [x_ij]_{m×n}. Formül: X = \big[x_{ij}\big]_{m\times n} Anchor: Puška et al. 2024, p.4 Eq.(6); Çemrek 2025, Eq.(6)
2. 2.Adım 2 (F2): Step 2: Dual normalisation. Primary n_ij: benefit x_ij/max, cost min/x_ij. Complement (n_ij)': benefit min/x_ij, cost x_ij/max. Formül: n_{ij} = \begin{cases} x_{ij}/\max x_{ij} & j\in J^{+}\\ \min x_{ij}/x_{ij} & j\in J^{-}\end{cases};\quad (n_{ij})' = \begin{cases} \min x_{ij}/x_{ij} & j\in J^{+}\\ x_{ij}/\max x_{ij} & j\in J^{-}\end{cases} Anchor: Puška 2024, p.4 Eqs.(7)-(8); Çemrek 2025, Eqs.(7)-(8)
3. 3.Adım 3 (F3): Step 3: Deviation from maximum, weighted: θ_ij = Σ_j [(1 − n_ij)·w_j] and (θ_ij)' = Σ_j [(1 − (n_ij)')·w_j]. Formül: \theta_{i} = \sum_{j=1}^{n} (1 - n_{ij})\,w_{j},\quad \theta'_{i} = \sum_{j=1}^{n} (1 - (n_{ij})')\,w_{j} Anchor: Puška 2024, p.5 Eqs.(9)-(10); Çemrek 2025, Eqs.(9)-(10)
4. 4.Adım 4 (F4): Step 4: RAWEC index Q_i = (θ'_i − θ_i) / (θ'_i + θ_i) ∈ [-1, 1]; descending ranking. The higher Q_i, the better the alternative. Formül: Q_{i} = \dfrac{\theta'_{i} - \theta_{i}}{\theta'_{i} + \theta_{i}},\quad Q_{i} \in [-1, 1] Anchor: Puška 2024, p.5 Eq.(11); Çemrek 2025, Eq.(11)

Commonly paired with

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

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