MEREC Method
Method Based on the Removal Effects of Criteria
MEREC (Method based on the Removal Effects of Criteria) is an objective weighting method for MCDM. It determines the importance of each criterion by measuring how much the overall performance of alternatives changes when that criterion is removed. A larger removal effect indicates a more important criterion.
Video Demonstration
Step-by-Step Algorithm
Form the decision matrix
Create the decision matrix with $m$ alternatives and $n$ criteria :
\[ X=\begin{bmatrix} x_{11} & x_{12} & \cdots & x_{1n}\\ x_{21} & x_{22} & \cdots & x_{2n}\\ \vdots & \vdots & \ddots & \vdots\\ x_{m1} & x_{m2} & \cdots & x_{mn} \end{bmatrix} \]
$x_{ij}$ presents the performance value of ith alternative on jth criterion, m and n are the numbers of alternatives and criteria respectively.
| Alternative | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $A_1$ | 10 | 20 | 30 |
| $A_2$ | 15 | 25 | 35 |
| $A_3$ | 25 | 15 | 35 |
Normalize the decision matrix
For benefit criterion :
For cost criterion :
Where $r_{ij}$ is the normalized value of alternative $A_i$ for criterion $C_j$.
C₁ and C₃ are benefit criteria (divide min by value). C₂ is a cost criterion (divide value by max).
| Alternative | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $A_1$ | 1.0000 | 0.8000 | 1.0000 |
| $A_2$ | 0.6667 | 1.0000 | 0.8571 |
| $A_3$ | 0.4000 | 0.6000 | 0.8571 |
Calculate the overall performance score
The overall performance score of alternative $A_i$ is calculated as :
Where $n$ is the number of criteria.
| Alternative | Performance ($S_i$) |
|---|---|
| $A_1$ | 0.0718 |
| $A_2$ | 0.1712 |
| $A_3$ | 0.4234 |
Calculate performance after removing each criterion
For each criterion $C_j$, remove it from the calculation and recalculate the performance of every alternative :
Where $S_{ij}'$ represents the performance of alternative $A_i$ when criterion $C_j$ is removed.
| Alternative | $S_{i1}'$ (without $C_1$) | $S_{i2}'$ (without $C_2$) | $S_{i3}'$ (without $C_3$) |
|---|---|---|---|
| $A_1$ | 0.0718 | 0.0000 | 0.0718 |
| $A_2$ | 0.0501 | 0.1712 | 0.1268 |
| $A_3$ | 0.2003 | 0.3054 | 0.3891 |
Total of the absolute deviations
The removal effect of criterion $C_j$ for alternative $A_i$ is :
For each criterion, sum its removal effects across all alternatives :
Where $E_j$ represents the total removal effect of criterion $C_j$.
| Alternative | $E_{i1}$ | $E_{i2}$ | $E_{i3}$ |
|---|---|---|---|
| $A_1$ | 0.0000 | 0.0718 | 0.0000 |
| $A_2$ | 0.1211 | 0.0000 | 0.0444 |
| $A_3$ | 0.2231 | 0.1180 | 0.0343 |
| Total ($E_j$) | 0.3441 | 0.1898 | 0.0787 |
Weights of criteria
The final MEREC weight of criterion $C_j$ is :
The weights satisfy :
| Criterion | Removal Effect ($E_j$) | Weight ($w_j$) |
|---|---|---|
| $C_1$ | 0.3441 | 0.5616 |
| $C_2$ | 0.1898 | 0.3099 |
| $C_3$ | 0.0787 | 0.1285 |
Sum check: $0.5616 + 0.3099 + 0.1285=1.0000$ ✓