MAUT Method
Multi-Attribute Utility Theory
MAUT (Multi-Attribute Utility Theory) is an MCDM method used to evaluate and rank alternatives. It converts the performance of each alternative into utility values, assigns weights to the criteria, and combines them into an overall utility score.
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
Normalize the decision matrix according to the type of criterion. For a benefit criterion :
For a cost criterion :
Where $r_{ij}$ is the normalized performance of alternative $A_i$ for criterion $C_j$.
| Alternative | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $A_1$ | 0.0000 | 0.5000 | 0.0000 |
| $A_2$ | 0.3333 | 0.0000 | 1.0000 |
| $A_3$ | 1.0000 | 1.0000 | 1.0000 |
Marginal utility score
The marginal utility score of alternative $A_i$ for criterion $C_j$ is calculated using the normalized value $r_{ij}$ :
Where $u_{ij}$ is the utility score and $r_{ij}$ is the normalized value of alternative $A_i$ with respect to criterion $C_j$.
| Alternative | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $A_1$ | 0.0000 | 0.1661 | 0.0000 |
| $A_2$ | 0.0687 | 0.0000 | 1.0048 |
| $A_3$ | 1.0048 | 1.0048 | 1.0048 |
Final utility score and ranking
The final utility score of alternative $A_i$ is calculated by summing the weighted marginal utility scores across all criteria :
Where $U_i$ is the overall utility score of alternative $A_i$.
Rank the alternatives according to their final utility scores :
| Alternative | Utility Score ($U_i$) |
|---|---|
| $A_1$ | 0.0334 |
| $A_2$ | 0.1215 |
| $A_3$ | 1.0048 |
Final ranking: $A_3 \succ A_2 \succ A_1$