Dear Sandile Thamie Mhlanga and Manoj Lall

I have read your paper

Influence of Normalization Techniques on Multicriteria Decision-making Methods

My comments:

1- In page 4 you say “The AHP method is used to solve complex decisions by arranging the alternatives into hierarchical form”

Precisely, due to that AHP works with a lineal hierarchy and thus, without any transversal and down-bottom-up links, it is not suitable to solve complex problems. The method was conceived to work with projects that follow the top-down military lineal approach, and at the time it was developed, it was ‘discovered’ by companies working in that mode since centuries, and hence its success.

But that happened in the 70s, more than 50 years ago, when companies’ structures changed due to the necessity to incorporate multiple interrelations, and adopting another type of organizational structure, pressured by social and environmental organizations. You can read this in any book on industrial organization, and gradually, the AHP method ceased to represent reality.

It is not coincidence that years later Saaty developed ANP, which working with a network, is able to address medium complex problems. Therefore, this inability to solved complex scenarios is not a failure of the AHP method, simply because it was not conceived for that.

2. Page 4- “To solve complex decisions by means of the AHP method, the alternatives are arranged into hierarchical form”

I don’t think this is correct. The hierarchical structure starts with a main and unique objective, down to criteria and sub criteria, and further down to alternatives and sub alternatives.

3- In page 10 “The results obtained highlight the importance of normalization in the AHP-VIKOR approach. It is apparent that a applying a particular normalization technique may result in different outcomes”

This is your conclusion, but you did not need to perform this study to demonstrate it, since it is a very-well phenomenon in MCDM.

The causes for this discrepancy, as per my reasoning, is that the distances between alternatives are not proportional, and then, in a method like VIKOR or TOPSIS, that work based on distances, this is a fundamental reason for the discrepancy, and consequently, the different in rankings do not depend on the normalization method used, but in the MCDM method employed.

There is a tangible proof of this. If you solve a problem using Linear Programming (LP)/SIMUS method, all rankings are the same, irrelevant of the normalization employed, because LP does not work with distances, with the possible exception of using max-min, and in some problems.

Therefore, in my opinion, what would be a relevant progress is determining which normalization method is the most appropriate for each MCDM method.

Hope these comments may help you

Nolberto Munier