Dear Mr. Duong and coauthors

I have read your article: “Expert opinion-based multi objective optimization: an application in plasma coating technology”

And here are my comments:

1- In page 1 you say: “A very important problem that should be done when solving multi-objective optimization problems is determining the weight for criteria [3]”

Yes, it is, but unfortunately, most weights are artificial or subjective, without any rational and /or mathematical support. There are also objective weights that are grounded on statistics, which are safer than subjective.

Some MCDM methods work without weights; however, they are computed internally by the software based on data imputed. That is, there is no subjectivity.

Of course, the opinion of the DM is very important regarding relative importance of each criterion, and it is always necessary. However, it must be rational and well documented, that is, considering many aspects, which unfortunately are not always taken into account, and based, as in most cases, for personal and arbitrary values, more related with the mood of the DM than with the problem.

2- “The sum of weights of the criteria is 1”

Correct, but this means that if you increase criterion C1, all other criteria will decrease proportionally. Is this correct in your case? I am not in your field, so I am not arguing on technical issues, but it does not seem natural that if you increase ‘spray distance’ for instance, “current intensity’ and ‘powder feed flow’, must decrease, proportionally.

3- In page 3. Please correct error in Podgorica (Turkey); it should be Podgorica (Montenegro)

4- In Section 3 you say “The main purpose of this study is to apply the FUCOM method to determine the weight of criteria for solving the multi-objective optimization problem”

I understood that the main objective is to determine the value of the input parameters (x1, x2 and x3), not the weights of criteria.

Anyway, the problem is really very interesting and there is no doubt that you get with the analytical procedure a very good level of closeness with the experimental values.

I solved your problem using the SIMUS method, with the same data and without any type of weights.

My results are very similar to yours, as follows:

Input parameters Your calculation My calculation Original average values

📷1 568.69 (*) 580.50 550.03

📷2 31.87 (*) 29.79 30.31

📷3 170.19 (*) 154.58 160.65

(*) Unfortunatelly I couldn’t find the input parameters values from your calculation. You only mention average of optimal values, and don’t indicate where they come from.

Regarding degree of compliance of criteria, my values are (obtained by SIMUS):

Output parameters

Result % of fit

y1 min = 462.09 0.83

y1 max= 689.45 0.96

y2min= 13.44 0.98

y2max= 45.89 0.98

y3min= 102.17 0.92

y3max= 248.05 0.92

I hope that these comments may help your research

Of course, you answer will be welcome

Nolberto Munier