Dear Jonathas Vinícius Gonzaga Alves Araujo , Miguel Ângelo Lellis Moreira , Carlos Francisco Simões Gomes , Marcos dos Santos, Luana de Azevedo de Oliveira , Gabriel Pereira de Oliveira Capela , Emerson Hissao Kojima , Daniel Augusto de Moura Pereira

I have read your paper

Multi-criteria Decision Support Method AHP-TOPSIS-2N applied in bids to improve the control of public expenses

Here my comments.

1- In page 2 you state “…. and the decision will be based only on mathematical models. As a result, the verdict is accurate and impartial without the influence of personal preferences’

So, the final decision is ONLY based on what a mathematical process say? What is the function of the Decision Maker (DM) then? Just to invent weights for criteria, based on his intuition and then apply TOPSIS?

There are many things that cannot be established beforehand in a MCDM problem. The DM function is to give stakeholders an answer based on a mathematically feasible solution, that he has studied, analyzed, corrected some data, if necessary, considered exogenous factors, etc., and finally give his recommendation.

Please, read again what I have underlined in your exposition. Using AHP is 100% preferences and therefore the verdict is far from being accurate.

2- In page 2 “weighted by a specialist”

According to this, the DM must be a multiple specialist in engineering, economics, financing, health, environment, social issues, etc., areas that must correspond to different criteria. It is really hard to understand how the reviewers of ‘Procedia Computer Science 221’ accepted this, which is clearly false.

3- In page 2 “Thus, it is up to the decision analysis process, above all, as a tool to assist the decision agent”

In this I agree with you

4- In page 3 “The method is based on the dissolution and synthesis of the relationships between the criteria”

Not really. The methods is based on comparing criteriaon a single basis, as long as they are independent, consequently without relationships. This was clearly established by Saaty. In practically all problems, there are relationships between criteria. Presumably, this was the reason by which Saaty developed the ANP method, years later.

5- In page 4” The great benefit of the AHP method is to enable its users to assign relative weights to multiple attributes or multiple alternatives to a given attribute while performing a peer-to-peer comparison between them [20]”

Sorry, I don’t understand what you intend to say.

By the way, the DM does not assign weights to attributes, but to criteria. Attributes are the characteristics of the series of values within a criterion

6- Page 5 “Expresses the score of each alternative referring to each criterion, demonstrating how much the alternative influences or is influenced by the others”

The first par of your sentence is correct, since the performance value (It is not a score), indicates the contribution of each alternative to a certain criterion, but the second part is incorrect.

How a performance value for alternative A may influence the performance value for alternative B? And if both alternatives are different? For instance, A may be a cosmetic product and B a food product, and the criterion being unitary cost of each one.

7- Page 5 “To exemplify practically how the hybrid method AHP-TOPSIS-2N can be advantageous and of great relevance in the decision-making process in the bidding procedures,”

Wouldn’t it be better to wait that people using the method say that, instead of its authors?

Please, don’t assert something that you cannot prove!

8- Page 5 “The criteria chosen for the evaluation were: price, consumption, maximum speed, power, and comfort”

See what I said before? You cannot use AHP in this problem since all criteria are interrelated.

The explanation is simple: You can certainly compare from the economic point of view, price to power and say for instance that ‘Price is 3 times more important than power’

However, what you do not consider, is that in a certain extent price depends on power. Therefore, where do you compute the contribution of power that intervenes on price? This is why pair-wise comparison is not applicable here.

9- “The tool also has the option of using other variations of the TOPSIS method or other ways of obtaining the weights of the criteria”

Correct, and why you did not use objective weights like entropy, standards deviations or MEREC?

10- Your system uses two normalization processes, but you never explained why and which they are, since are many, therefore the reader is forced to believe what you put in Table 4.

11- Page 6 “bringing the user greater confidence and security.”

Another self-praise? This is not allowed in scientific papers

I hope my comments can help you

Nolberto Munier