DEMATEL Method
Decision-Making Trial and Evaluation Laboratory
DEMATEL (Decision-Making Trial and Evaluation Laboratory) is an MCDM method used to analyze cause-and-effect relationships among criteria. It identifies which criteria are causes and which are effects, and measures their relative importance within the system.It was developed by the Battelle Memorial Institute's Geneva Research Centre in 1972, under the direction of Fontela and Gabus . DEMATEL uses expert judgments to quantify the direct and indirect influences between criteria and represents them through a causal relationship diagram.
Video Demonstration
Step-by-Step Algorithm
Construct the direct-relation matrix
Experts evaluate the degree of direct influence of criterion \(i\) on criterion \(j\). The direct-relation matrix is :
\[ X=\begin{bmatrix} 0 & x_{12} & \cdots & x_{1n}\\ x_{21} & 0 & \cdots & x_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ x_{n1} & x_{n2} & \cdots & 0 \end{bmatrix} \]
Where \(x_{ij}\) represents the direct influence of criterion \(i\) on criterion \(j\), and \(x_{ii}=0\).
0=no influence, 1=low influence, 2=medium influence, 3=high influence, 4=very high influence .
| Criterion | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $C_1$ | 0 | 3 | 2 |
| $C_2$ | 2 | 0 | 1 |
| $C_3$ | 1 | 2 | 0 |
Normalize the direct-relation matrix
The normalization factor is calculated as :
The normalized direct-relation matrix is then obtained as :
Where \(X\) is the direct-relation matrix and \(s\) is the normalization factor.
Normalization Factor Calculation:
| Metric | $C_1$ | $C_2$ | $C_3$ | Max |
|---|---|---|---|---|
| Row Sums | 5 | 3 | 3 | 5 |
| Col Sums | 3 | 5 | 3 | 5 |
Normalized Matrix ($N$):
| Criterion | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $C_1$ | 0 | 0.60 | 0.40 |
| $C_2$ | 0.40 | 0 | 0.20 |
| $C_3$ | 0.20 | 0.40 | 0 |
Calculate the total-relation matrix
The total-relation matrix includes both direct and indirect influences:
Where \(I\) is the identity matrix.
Identity Matrix ($I$):
| 1 | 0 | 0 |
| 0 | 1 | 0 |
| 0 | 0 | 1 |
Normalized Matrix ($N$):
| 0 | 0.60 | 0.40 |
| 0.40 | 0 | 0.20 |
| 0.20 | 0.40 | 0 |
Inverse Matrix $(I-N)^{-1}$:
| Criterion | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $C_1$ | 1.7969 | 1.4844 | 1.0156 |
| $C_2$ | 0.8594 | 1.7969 | 0.7031 |
| $C_3$ | 0.7031 | 1.0156 | 1.4844 |
Total-Relation Matrix ($T=N \times (I-N)^{-1}$):
| Criterion | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $C_1$ | 0.7969 | 1.4844 | 1.0156 |
| $C_2$ | 0.8594 | 0.7969 | 0.7031 |
| $C_3$ | 0.7031 | 1.0156 | 0.4844 |
Calculate the threshold value
The threshold value is calculated as the average of all elements of the total-relation matrix \(T\) :
Where \(t_{ij}\) represents the total influence of criterion \(i\) on criterion \(j\), and \(n\) is the number of criteria.
The threshold value \(\alpha\) is used to identify significant relationships :
| Metric | Value |
|---|---|
| Sum of all elements in $T$ | 7.8594 |
| Threshold ($\alpha$) | 0.8733 |
Cause and effect relationship
The sum of the columns gives \(r_i\) :
The sum of the rows of the total-relation matrix gives \(c_i\) :
The prominence of criterion \(i\) is :
A higher \(r_i+c_i\) indicates that the criterion has greater overall importance and involvement in the system.
The causal relation of criterion \(i\) is :
The value determines whether the criterion belongs to the cause or effect group.
Criteria with positive values influence other criteria more than they are influenced by them, while negative values indicate the opposite.
| Criterion | $r_i$ | $c_i$ | $r_i+c_i$ | $r_i-c_i$ |
|---|---|---|---|---|
| $C_1$ | 3.2969 | 2.3594 | 5.6563 | 0.9375 |
| $C_2$ | 2.3594 | 3.2969 | 5.6563 | -0.9375 |
| $C_3$ | 2.2031 | 2.2031 | 4.4063 | 0.0000 |
Cause Group ($r_i - c_i >0$): $C_1$ influences the other criteria.
Effect Group ($r_i - c_i < 0$): $C_2$ is influenced by other criteria.
Borderline: $C_3$ has exactly equal sending and receiving influences.
Prominence: $C_1$ and $C_2$ have the highest prominence (5.6563), meaning they are the most important criteria overall in the system.