Your Decision Engine.Decide Faster. Better. Fairer.TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) is a
multi-criteria decision-making method that ranks options based on how close they are to the
ideal
choice. It’s a simple, transparent way to make better decisions using data and
mathematics.
TOPSIS Methodology
This grid contains 5 rows (R1 to R5) and 5 columns (C1 to C5), where each cell
value \( x_{ij} \) represents the performance of option \( i \) under criterion \( j \). Below the
grid, the Weight row assigns importance to each criterion, and the Impact row
indicates whether the criterion is beneficial (+) or costly (–), affecting how ideal solutions are
determined.
\[
\begin{aligned}
r_{ij} &= \frac{x_{ij} * w_{j}}{\sqrt{\sum_{k=1}^{m} x_{kj}^2}}, \\
i &= 1, 2, \dots, m, \\
j &= 1, 2, \dots, n
\end{aligned}
\]
Step 1 : Calculating Normalized Matrix
In the TOPSIS method, the first step is to normalize the decision matrix
so that different criteria with varying units and scales can be compared fairly. This is
done by dividing each value in the matrix by the square root of the sum of squares of all
values in its column. The result is a unitless normalized matrix where each criterion
contributes proportionally, allowing for meaningful multi-criteria analysis.
Step 2 : Defining Ideal Best and Worst and Calculating Euclidean Distances
Based on the impact parameter (+ for benefit , – for cost), the Ideal Best
is chosen as the maximum value for benefit criteria and minimum for cost criteria. The Ideal
Worst is the reverse. Using these, we calculate the Euclidean distance of each alternative
from both ideal points to measure how close each is to the best and worst possible
solutions.
The TOPSIS score for each alternative is calculated by dividing its
distance from the Ideal Worst by the total of its distances from both the Ideal Best and the
Ideal Worst. This gives a value between 0 and 1, where a higher score indicates the
alternative is closer to the ideal solution and thus more favorable.
Implementation
Enter the number of options and criteria you want to
compare. Set the weight and impact of each criterion, input your data, and instantly get a ranked
list of the best choices using the TOPSIS decision-making method. (Make sure weight of each of your criteria is less than 1 and greater than 0. The sum of all weights must add to 1 for correct functioning)
