RAWEC - Eşit Kriter Ağırlıklarıyla Alternatiflerin Sıralanması

Formül adımları

Analiz motorunun yöntem bildirimindeki (manifest F.steps) adımlar; raporlardaki formüllerle aynı kaynaktır.

1. Adım 1 — Başlangıç karar matrisi X = [x_ij]_{m×n}.

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

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

2. Adım 2 — Çift normalleştirme. Birincil n_ij: fayda x_ij/max, maliyet min/x_ij. Tamamlayıcı (n_ij)': fayda min/x_ij, maliyet x_ij/max.

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

   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}

3. Adım 3 — Maksimumdan ağırlıklı sapma: θ_ij = Σ[(1 − n_ij)·w_j] ve (θ_ij)' = Σ[(1 − (n_ij)')·w_j].

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

   \theta_{i} = \sum_{j=1}^{n} (1 - n_{ij})\,w_{j},\quad \theta'_{i} = \sum_{j=1}^{n} (1 - (n_{ij})')\,w_{j}

4. Adım 4 — RAWEC indeksi Q_i = (θ'_i − θ_i) / (θ'_i + θ_i) ∈ [-1, 1]; azalan sıralama. En yüksek Q_i en iyi alternatif.

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

   Q_{i} = \dfrac{\theta'_{i} - \theta_{i}}{\theta'_{i} + \theta_{i}},\quad Q_{i} \in [-1, 1]

Sezgi

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

Sonucu okuma: 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.

Varsayımlar

• 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)

Ne zaman kullanılmaz

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

Sınırlılıklar

• 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)

Sık yapılan hatalar

• D_i = 0: alternatif her kriterinde 1. sırada - W = +∞. En iyi sıra göstergesiyle ele alın.