RAWEC - Ranking Alternatives With Equal Criteria weights

Overview

W_i > 0 (or +∞ if alternative ranks 1st on all criteria). Higher W means smaller average deviation from rank-1 ideal. RAWEC is explicitly designed for situations where no reliable criterion weights are available - it assumes equal weighting and measures how consistently an alternative is near the top across all criteria.

Output

utility, higher 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

How it works

1. 1

   Construct the initial decision matrix X = [x_ij]_{m×n}.

   $$X=[x_{ij}{]}_{m\times n}$$

   Puška et al. 2024, p.4 Eq.(6); Çemrek 2025, Eq.(6)

2. 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.

   $$n_{ij}=\{\begin{array}{ll}{x}_{ij}/\max x_{ij}& j\in J^{+}\\ \min x_{ij}/x_{ij}& j\in J^{-}\end{array};(n_{ij}{)}^{\prime }=\{\begin{array}{ll}\min x_{ij}/x_{ij}& j\in J^{+}\\ x_{ij}/\max x_{ij}& j\in J^{-}\end{array}$$

   Puška 2024, p.4 Eqs.(7)-(8); Çemrek 2025, Eqs.(7)-(8)

3. 3

   Deviation from maximum, weighted: θ_ij = Σ_j [(1 − n_ij)·w_j] and (θ_ij)' = Σ_j [(1 − (n_ij)')·w_j].

   $${\theta }_i=\sum _{j=1}^n(1-n_{ij})w_j,{\theta }_i^{\prime }=\sum _{j=1}^n(1-(n_{ij}{)}^{\prime })w_j$$

   Puška 2024, p.5 Eqs.(9)-(10); Çemrek 2025, Eqs.(9)-(10)

4. 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.

   $$Q_i=\frac{{\theta }_i^{\prime }-{\theta }_i}{{\theta }_i^{\prime }+{\theta }_i},Q_i\in [-1,1]$$

   Puška 2024, p.5 Eq.(11); Çemrek 2025, Eq.(11)

Look elsewhere when

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)

Edge cases and pitfalls

• D_i = 0: alternative ranks 1st on every criterion - W = +∞. Handle as best rank with indicator.

Works with

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