EDAS Method
Evaluation Based on Distance from Average Solution
EDAS (Evaluation based on Distance from Average Solution) is an MCDM method that evaluates alternatives according to their positive distance from the average solution (PDA) and negative distance from the average solution (NDA). Alternatives with higher PDA and lower NDA are preferred.
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 |
Calculate the average solution
The average solution for each criterion is calculated as :
The vector of average solutions is :
The average solution represents the reference point for evaluating the alternatives.
| Metric | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| Average ($AV_j$) | 16.6667 | 20.0000 | 33.3333 |
Calculate the positive distance from average (PDA)
For a beneficial criterion :
For a non-beneficial criterion :
PDA measures how much an alternative performs better than the average solution.
C₁, C₃: benefit ($x_{ij} >AV_j$ contributes). C₂: cost ($x_{ij} < AV_j$ contributes).
| Alternative | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $A_1$ | 0 | 0 | 0 |
| $A_2$ | 0 | 0 | 0.0500 |
| $A_3$ | 0.5000 | 0.2500 | 0.0500 |
Calculate the negative distance from average (NDA)
For a beneficial criterion :
For a non-beneficial criterion :
NDA measures how much an alternative performs worse than the average solution.
C₁, C₃: benefit ($x_{ij} < AV_j$ contributes). C₂: cost ($x_{ij} >AV_j$ contributes).
| Alternative | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $A_1$ | 0.4000 | 0 | 0.1000 |
| $A_2$ | 0.1000 | 0.2500 | 0 |
| $A_3$ | 0 | 0 | 0 |
Weighted sum of PDA and weighted sum of NDA
Multiply the positive and negative distances by the criterion weights :
where \(w_j\) is the weight of criterion \(j\).
| Alternative | $SP_i$ | $SN_i$ |
|---|---|---|
| $A_1$ | 0 | 0.2983 |
| $A_2$ | 0.0036 | 0.1230 |
| $A_3$ | 0.4178 | 0 |
Normalize SP and SN
The normalized positive distance is :
The normalized negative distance is :
A higher \(NSP_i\) and \(NSN_i\) indicate better performance.
$\max_i SP_i=0.4178$, $\max_i SN_i=0.2983$.
| Alternative | $NSP_i$ | $NSN_i$ |
|---|---|---|
| $A_1$ | 0 | 0 |
| $A_2$ | 0.0086 | 0.5876 |
| $A_3$ | 1.0000 | 1.0000 |
Appraisal score and ranking
The final appraisal score is :
The appraisal score combines the positive and negative distances into one overall measure.
The alternatives are ranked according to their appraisal scores :
| Alternative | $AS_i$ |
|---|---|
| $A_1$ | 0 |
| $A_2$ | 0.2981 |
| $A_3$ | 1.0000 |
Final ranking: $A_3 \succ A_2 \succ A_1$