Dear Hoang Xuan Thinh, Nguyen Trong Mai, Nguyent Trong Mai

I read your paper

Comparison of two methods in Multi-Criteria Decision-Making: Application in transmission rod material selection

These are my comments

1- In the abstract, I guess you are referring to connecting rods

You only explain the action (minimum or maximum), only in two criteria out of nine

2- In page 1 you mention different procedures that generate RR, but forget the most important, that is, the RR when you add or delete alternatives

3- - The MEREC method is very good, however, I remind you that if the problem has say, 8 criteria, the method gives incomplete weights, since it always removes one of them, equivalent to solving 8 different, albeit very similar, problems.

4- “The Mean weight method is the one where the weighted values of the criteria are equal, i.e. equal to 1/n”

I am afraid that you are mistaken. What you describe is all criteria having equal weighted values, very unusual indeed.

The mean weighted methods is the sum of the product of each weight by the respective value of a criterion

5- In page 2 you say “Let’s suppose that m alternatives should be ranked, each of which includes j criteria, let yij be the value of criterion j at alternative i, with i = 1÷m, j = 1÷n”

Normally you use the same weights only for criteria., not for alternatives

“These methods have also been evaluated to be equal[1]y effectiveas many other MCDM methods”

And how do you know that they are effective if you do not have a yardstick to compare them to?

In addition, the fact that two or there or more methods are similar in their rankings, means nothing. Same for PIV and FUCA.

“The selection of a steel considered «the best» must consider all nine criteria simultaneously.’

Agreed

6- In my opinion, formulas 7,8 and 9 are incorrect. Ej is always negative since it finds the ln of decimals; by the way, I have never seen this formula for Shannon entropy. I understand that the correct formula only involves the first term

In addition, you do not consider the average value of ej because it has to be multiplied by (– 1/ ln(n)), where ‘n’ is the number of alternatives. Because of this your values are incorrect.

In formula 9, ‘w ‘ is not the weight, but the information content (I), that is the complement to 1 of ej

In Table 2, the means for criteria is the same? How come?

In page 6 “the ranks of types of steel are completely identical when using two methods of weight determination as Mean weight method and MEREC weight method”

In my opinion shouldn’t be identical, because you are comparing different matrices. Remember that in all MCDM methods you compare identical matrices.

7- In my opinion, MEREC is not an objective method, since the DM decides to remove one criterion at the time, therefore, in each run each matrix is different

I hope these comments may help you

Nolberto Munier