DEMATEL - Karar Verme Deney ve Değerlendirme Laboratuvarı

Formül adımları

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

1. Adım 1 — Doğrudan ilişki matrisi A.

   $$A=[a_{ij}{]}_{n\times n},a_{ij}\in \{0,1,2,3,4\}$$
   LaTeX

   A = [a_{ij}]_{n\times n},\quad a_{ij}\in\{0,1,2,3,4\}

2. Adım 2 — Normalleştirilmiş matris X.

   $$X={\displaystyle \frac{A}{max({max}_i{\sum }_j{a}_{ij},{max}_j{\sum }_i{a}_{ij})}}$$
   LaTeX

   X = \dfrac{A}{\max\big(\max_{i}\sum_{j} a_{ij},\ \max_{j}\sum_{i} a_{ij}\big)}

3. Adım 3 — Toplam ilişki matrisi T.

   $$T=X(I-X{)}^{-1}$$
   LaTeX

   T = X(I - X)^{-1}

4. Adım 4 — Etkenlik D+R, ilişki D−R.

   $$D_i=\sum _j{t}_{ij},R_j=\sum _i{t}_{ij};\text{Prominence}=D+R,\text{Relation}=D-R$$
   LaTeX

   D_{i}=\sum_{j} t_{ij},\ R_{j}=\sum_{i} t_{ij};\ \text{Prominence}=D+R,\ \text{Relation}=D-R

5. Adım 5 — DEMATEL ağırlıkları.

   $$\text{optional: }{w}_j={\displaystyle \frac{D_j+R_j}{{\sum }_k(D_k+R_k)}}$$
   LaTeX

   \text{optional: }w_j=\dfrac{D_j+R_j}{\sum_k(D_k+R_k)}

Sezgi

DEMATEL models how factors influence one another. Its primary result is a causal map: prominence shows total involvement and relation separates net causes from net effects. It does not produce an alternative ranking; prominence-normalized weights are optional post-processing only.

Sonucu okuma: DEMATEL's primary result is a causal map: criteria with E_i > 0 are net causes and criteria with E_i < 0 are net effects. Criterion weights are absent by default; select prominence_normalized only when that later post-processing convention is scientifically appropriate.

Varsayımlar

• The input is a square directed factor-influence matrix
• Direct influences are finite and non-negative with a zero diagonal
• The normalized matrix has spectral radius below one

Ne zaman kullanılmaz

• A defensible square direct-influence matrix cannot be elicited
• The decision requires an alternative ranking rather than a causal influence map

Sınırlılıklar

• Requires a defensible direct-influence matrix
• Does not intrinsically rank alternatives or provide criterion weights

Sık yapılan hatalar

• X'in spektral yarıçapı ≥ 1: (I−X)^{−1} ıraksıyor - etki değerlerini azaltın veya verileri kontrol edin.