Dear Nuh Keleş

I have read your paper

Measuring performances through multiplicative functions by modifying the MEREC method: MEREC-G and MEREC-H

My comments

1- In page 3 you say “Various methods such as the objective, subjective and integrated have been developed. Subjective weighting techniques are often problematic due to the need for truly expert knowledge in the field to accurately assign importance to criteria”

On what basis you assert that a truly expert assures accurately measurement of criteria?

What happens if another truly expert on the same field assigns different importance? Who is right?

Nobody knows. Even the same first expert, may have a change of mind a little later and change the original value he assigned before. Therefore, there is no guarantee of reproducible evaluations.

2- In page 3 “The working principle of the objective methods is based on the evaluation of the scores of the previously determined alternatives according to the criteria”

In my opinion, this is incorrect. Objective methods are not based on the score of the alternatives, and they couldn’t, because they are still unknown!

They are based on the performance values, that constitute the criteria series of values, one for each alternative. And the weight of each criterion depends on the discrimination of those series of values, or amount of information (Shannon’s theorem). Similar when using standard deviation.

3- “The working principle of the objective methods is based on the evaluation of the scores of the previously determined alternatives according to the criteria”

The scores are the final values of the alternatives, so, no method can be based on them. The value that each alternative has for each criterion is called ‘performance value’. Apparently, you confuse scores with performance values.

4” page 3 “A criterion has an immense weight when its removal leads to a higher impact on alternatives’ total performances. ”

Again, alternatives performances are their values on each criterion. You classify alternatives according to their SCORES not on PERFORMANCES (except in SAW). The higher the score the more important an alternative. The deceasing sequencing of score is what is called ‘Ranking’

5-“This perspective not only determines the objective weight of each criterion but may also make it easier for decisionmakers to exclude certain criteria from the decision-making procedure”

You cannot eliminate criteria, because like it or not, important or not, they are part of the problem. It is like saying that you can eliminate nails because they are not enough important part of the human body, and they are, since they can tell a lot about your health.

6- “The MEREC weights the criteria as an objective method proved to be reliable over a more traditional method as entropy and as a novel method applicable to be used for decision-making problems”

Yes, it is novel, but in my opinion incorrect. Why:

Be cause if you have say ,7 criteria and apply MEREC seven timers, you are solving seven different problems, not only one, because if you eliminate a criterion out of seven, the resulting six criteria decision making is different from the original. On what grounds can you explain this?

7-“The MEREC method is used to determine the weights for attributes/criteria in literature”

Attributes and criteria are not the same thing. Attributes refers to the characteristics of the series of values or performances within each criterion. For instance: Discrimination, integers, formulas, etc

8- In page 7. I have read many times step 3 and I still cannot understand it. Ok, you assign all criteria the someway, which is reasonable, then you remove one criterion, and according formula 4 you get a value for each alternative. My question is: Where formula 4 comes from?

Why, the weight of a criterion is given by 1 plus ln of the sum of 1 plus the average of the ln of the performance values? Who says that?

If there is a reason, and probably is, you have to explain it. Even the authors of MEREC do not explain the origin of that formula.

As I see it, in MEREC you compute the average value of each criterion based on its performance values.

It makes a lot of sense to think that by physically removing a criterion, the other criteria take new values because compensation, and that alternatives are affected by this procedure.

The process is in some ways similar to entropy, because both are looking for discrimination, however, in entropy you always work with the whole set of criteria. In my opinion, what you propose is very convenient, since obviously it is much easier to work with a geometric mean.

I hope these comments may help you

Nolberto Munier