WISP-S Method
Simplified Weighted Integrated Sum Product
WISP-S (Simplified Weighted Integrated Sum Product) is a simplified version of the WISP method. It reduces the computational complexity of the original WISP by using two utility indicators instead of four, making the method faster while maintaining similar ranking results.
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
\(r_{ij}\) is the normalized performance of alternative \(A_i\) for criterion \(C_j\).
| Alternative | $C_1$ | $C_2$ | $C_3$ |
|---|---|---|---|
| $A_1$ | 0.4000 | 0.8000 | 0.8571 |
| $A_2$ | 0.6000 | 1.0000 | 1.0000 |
| $A_3$ | 1.0000 | 0.6000 | 1.0000 |
Calculate the utility Measures
Unlike the original WISP method, WISP-S uses only two utility measures : the weighted sum difference and the weighted product ratio.
Weighted sum difference utility :
Calculate the difference between the weighted sum of normalized ratings for beneficial criteria and the weighted sum for non-beneficial criteria.
\(u_i^{sd}\) represents the difference between the weighted sums of beneficial and non-beneficial criteria.
Weighted product ratio utility :
Calculate the ratio between the weighted products of normalized ratings for beneficial and non-beneficial criteria.
\(u_i^{pr}\) represents the ratio between the weighted products of beneficial and non-beneficial criteria.
| Alternative | $u_i^{sd}$ | $u_i^{pr}$ |
|---|---|---|
| $A_1$ | 0.1915 | 0.1105 |
| $A_2$ | 0.3070 | 0.1548 |
| $A_3$ | 0.6786 | 0.4301 |
Recalculated utility measures values
The two utility measures are transformed into comparable values in the interval $[0,1]$ before they are combined into the overall utility.
Recalculated weighted sum difference :
Recalculated weighted product ratio :
\(\bar{u}_i^{sd}\) and \(\bar{u}_i^{pr}\) are the recalculated values of \(u_i^{sd}\) and \(u_i^{pr}\), respectively.
Max values: $\max u_i^{sd}=0.6786$, $\max u_i^{pr}=0.4301$
| Alternative | $\bar{u}_i^{sd}$ | $\bar{u}_i^{pr}$ |
|---|---|---|
| $A_1$ | 0.7098 | 0.7765 |
| $A_2$ | 0.7786 | 0.8075 |
| $A_3$ | 1.0000 | 1.0000 |
Overall utility and ranking
Calculate the overall utility of each alternative as the arithmetic mean of the two recalculated utility measures.
\(u_i\) is the final WISP-S utility value of alternative \(A_i\). A higher value indicates a better alternative.
Sort the alternatives according to their overall WISP-S utility values in descending order.
| Alternative | Utility ($u_i$) |
|---|---|
| $A_1$ | 0.7432 |
| $A_2$ | 0.7930 |
| $A_3$ | 1.0000 |
Final ranking: $A_3 \succ A_2 \succ A_1$