The ideal fraction method is a normalization technique used in multi-criteria decision-making. This method is applied to normalize values for a criterion that needs to be maximized (where higher values are better), transforming the original scores into a scale from 0 to 1. The idea is to compare the original values with the best (ideal) and worst possible values within the set of data, assigning relative scores.
Steps to apply the ideal fraction method
In this case, let’s go through the steps to apply the ideal fraction method:
1. Identify the maximum and minimum values in the set:
The original scores for the criterion to be maximized are 5, 7, and 10.
- Ideal value (maximum): The highest value is 10.
- Lowest value: The lowest value is 5.
2. Apply the ideal fraction normalization formula:
The formula for normalizing a criterion to maximize is:
Ni=(Xi−Xmin) / (Xmax−Xmin)
Where:
- Ni is the normalized score for option iii.
- Xi is the original score for option iii.
- Xmax is the maximum value among all options.
- Xmin is the minimum value among all options.
Example
Given 3 scores:
X1 = 5; X2= 7; X3 = 10
The ideal fraction is:
X1 = 0
X2 = (7 – 5) / (10 – 5) = 2 / 5 = 0.4
X3 = 1