DEMATEL - Decision Making Trial and Evaluation Laboratory

1. 1. Direct-relation matrix A from expert pairwise influence judgements.

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

2. 2. Normalised direct relation X = A / max(row sum, col sum).

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

3. 3. Total relation matrix T = X(I − X)^{−1}.

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

4. 4. Row sums D and column sums R; prominence D+R, relation D−R.

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

5. 5. Return the causal map; optionally derive prominence-normalized weights only when explicitly requested.

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