MOORA - Oran Analizine Dayalı Çok Amaçlı Optimizasyon

Formül adımları

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

1. Adım 1 — Vektör normalleştirmesi r_ij = x_ij / √(Σ x_ij²).

   $$r_{ij}={\displaystyle \frac{x_{ij}}{\sqrt{{\sum }_{i=1}^m{x}_{ij}^2}}}$$
   LaTeX

   r_{ij} = \dfrac{x_{ij}}{\sqrt{\sum_{i=1}^{m} x_{ij}^{2}}}

2. Adım 2 — Ağırlıklı normalleştirilmiş matris v_ij = w_j · r_ij.

   $$v_{ij}=w_j{r}_{ij}$$
   LaTeX

   v_{ij} = w_{j}\,r_{ij}

3. Adım 3 — Oran sistemi y_i = Σ_{j∈J⁺} v_ij − Σ_{j∈J⁻} v_ij.

   $$y_i=\sum _{j\in J^{+}}{v}_{ij}-\sum _{j\in J^{-}}{v}_{ij}$$
   LaTeX

   y_{i} = \sum_{j\in J^{+}} v_{ij} - \sum_{j\in J^{-}} v_{ij}

4. Adım 4 — y_i'ye göre azalan sıralama; en yüksek değer en iyi alternatif.

   $$\text{Rank descending: }{y}_{(1)}\ge y_{(2)}\ge \cdots \ge y_{(m)}$$
   LaTeX

   \text{Rank descending: } y_{(1)}\ge y_{(2)}\ge\cdots\ge y_{(m)}

Sezgi

Ratio system + reference point (vector normalisation). Output typically utility (higher value = preferred).

Sonucu okuma: y_i can be any real number. Higher y_i (Ratio System) means better. Lower d_i (Reference Point) means better. MOORA produces two rankings - Ratio System (RS) and Reference Point (RP). They may disagree; the full MULTIMOORA method resolves this via dominance theory.

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

• 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)

Sık yapılan hatalar

• Ağırlıksız MOORA kullanmak: seminal yöntem ağırlıklar kullanır; bazı uygulamalar bunları atlar ve farklı sıralama verir.