# 103

Dear Nazanin Vafaei, Rita A. Ribeiro, Luis M. Camarinha-Matos

I read your paper

Selecting Normalization Techniques for the Analytical Hierarchy Process

My comments

1- In the Abstract you say “Most MCDM methods implement normalization techniques to produce dimensionless data in order to aggregate/rank alternatives”

It is true that it produces dimensionless data but not for ranking alternatives, but to make possible the algebraic steps, since you cannot add apples and oranges.

2- “Each MCDM problem is defined by a decision matrix

that includes a set of alternatives Ai (i=1, …, m), criteria Cj (j=1,…, n), the relative importance of the criteria (or weights)”

This is not exactly true. Some MCDM methods do not use weights

3- In section 5, could you explain this “In the original illustrative example [2], four pairwise comparison matrices were defined (three pairwise comparison matrices for each criterion and one pairwise comparison matrix between criteria) for AHP method and then selected normalization techniques were used to rank the alternatives”

As far as I can see there are only three pair-wise comparisons.

How can you compare if using only one criterion?

Why is the pair-wise comparison between criteria? All are between criteria, if not how can you make comparison if you do not have at least two things to be compared?

4- And why do you need normalization if all values are numbers between 1 and 9?

I am not saying that you are wrong, simply I don’t understand

These are only a few comments. I hope they can help

Nolberto Munier