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I am a research student and stuck at a point in my work and want your help. I have three different variables for each node of my network (Energy, Traffic Load and Link quality). These three variables have different units. I want to add them linearly to get a grade or rating in range of (0,1) and assign it to a node. So what i did is i normalized these variables in (0-1) range by dividing them with their maximum values and and then added them together. I want to know whether its correct?

Energy = Energy(i)/Energy(max) [0,1]
Traffic Load = Traffic Load(i)/Traffic Load(max) [0,1]
Link Quality = Link Quality (i)/Link Quality(max) [0,1]
Grade = Energy + Traffic Load + Link Quality
sashkello
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hasanfarooq
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  • Your question is unclear. Why are you adding them? Why do you want to normalize them? What all in all are you doing? – sashkello May 04 '13 at 09:44
  • Actually my work is related to routing protocol. I want to form a route which has nodes with maximum grade or rating. So i want to assign rating to nodes of my network based on their above mentioned variables. I want to know mathematically speaking whether this is correct to add them after they have been scaled in [0,1] range. – hasanfarooq May 04 '13 at 09:47
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    You can add or divide of multiply whatever you want, I still don't see the point. If this is your way of finding the grade - so be it. Another question is how good it describes things, but this is another problem... – sashkello May 04 '13 at 09:50

1 Answers1

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There is simply no single “mathematically” correct way to derive a grade from several variables or dimensions. Without more information on the characteristics of your variables and what you are trying to achieve, it's difficult to provide any useful advice.

One important thing to note is that dividing by the maximum value is almost certainly a bad idea because it is very sensitive to outliers. Consider the following data set:

Energy      Load      Quality
     3         1            1
     1         3            1
     1         1            3
     1         1          100

Intuitively, if you think that the three variables are expressed on the same scale and are equally good measures of whatever you are after, you would want the first three entries to have the same overall grade and the fourth one to be either much larger or flagged as a measurement error but in fact the third one will be noticeably smaller and the fourth one only slightly higher than the third or second. Apart from the fourth entry, differences in quality have almost no influence on the overall grade because of the one entry with an extremely large value. That's probably not a desirable feature.

The answers to How to represent an unbounded variable as number between 0 and 1 also contain a lot of useful information regarding this problem (bringing whatever grade you come up with to the 0-1 range).

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Gala
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