Article Determination of Objective Weights Using a New Method Based on the Removal Effects of Criteria (MEREC)

Mehdi Keshavarz-Ghorabaee , Maghsoud Amiri , Edmundas Kazimieras Zavadskas , Zenonas Turskis and Jurgita Antuchevicienee

I have read this article and my comments are:

1- In your abstract you say “This method (MEREC), uses a novel idea for weighting criteria”

It is indeed a novel and attractive idea; however, I believe that in so doing, whatever the MCDM method used, the alternatives are evaluated not by the m criteria initially proposed, but by m-1, i.e., is a different problem from the original, and it happens m times. So, at the end, there will be m different problems. At no time the alternatives are evaluated for the whole set of criteria, as in all methods.

What the procedure does not take into account, is that not all criteria are the same. If there are say, 10 criteria, some of them, say 4, are responsible for the best selection and the ranking of alternatives These are the so called ‘Binding criteria’, but the other 6 are no-binding, that is, they have no participation on the solution. As you know, the binding criteria conform a closed space called polytope,where all the feasible solutions reside. The other 6 do not conform it.

Consequently, if one criterion is removed, it may belong to one of these two classes. If it is binding, its removal most possibly will provoke the forming of a different polytope and a new ranking. If the criterion removed belons to the no-binding criteria, its removal will not affect anything and the result will be the same as before.

2- Since MEREC is an objective method to determine criteria weights, it would be interesting to compare them with the corresponding entropy derived weights.

The paper mentions ‘validity’. How can a method be validated if there is not a yardstick to compare to or use as a reference?

3- In page 1 “MCDM methods provide us with a process that results in rational, explainable, and justifiabledecisions.”

Sorry, I don’t share these assertions. Truly, there are methods that are rational like PROMETHEE, VIKOR and others, but can you call AHP or ANP rational?

4- In page 2 “We can say that determination of criteria weights is one of the most critical and complicated processes in dealing with MCDM problems”

Yes, determining weights is very important, however, I don’t think that it is the most critical process.

In my humble opinion, that qualification belongs to ‘Modelling’; If you don’t have a good mathematical model representing the problem, what is the use in having good weights.? You will be solving a problem that does not exist, because it does not duly represent reality.

5- In page 2 “The main disadvantage of these methods is that they are not efficient enough when the number of criteria increases. In other words, expressing preferences is a mental task for decision-makers, and the accuracy of their preferences decreases by increasing the number of criteria”

Exactly! However, I would make a difference: Subjective weights, when they are a result on an analysis criteria by criteria, using common sense, knowledge, consultation with other people, and reasoning, can be very good and deemed reliable. Now, weights coming according the mood and intuition of a DM, and as a consequence of a pair-wise comparisons, are probably very unreliable.

6- In page 2 “Besides weighting each criterion, this perspective may help decision-makers to exclude some criteria from the decision-making process”

I am afraid I disagree. Criteria are originated by the joint work of the DM and the stakeholders; therefore, they reflect what they want or needed. If we remove a criterion because it got a low grade, we are not solving the problem holistically.

As an example, we could remove a criterion like ‘Noxious gas emissions’ because it has a small weight. When solving the problem, it could be that it is unfeasible, because the emissions are higher than allowed by international standards and regulations. Or, in a large project that involves displacing people, we can’t remove it, because it has effect on other criteria like costs, which in turn may affects other criteria.

The article mention causality, but ignores causality regarding other criteria.

7- In page 7 “In this study, a simple logarithmic measure is used with equal weights to calculate alternatives’ performances”

Performance regarding what?

I don’t think that the normal reader will understand what is an alternative performance, let alone the use of a logarithmic expression. In my opinion it needs explanation. Most readers are not mathematicians.

8- In page 8 “Unlike many other studies, we transform all the criteria into the minimization type criteria”

Why?

9- On page 17 “We can claim that introducing new MCDM methods based on novel perspectives could ensure the robustness of results. Specifically, by integrating weighting methods, decision-makers can obtain weights that are more reliable”

Wouldn’t be better not to use weights, as in Linear Programming, where the weights are computed iteratively by the Simplex algorithm?

Of course, it could be a gross error not to consider the opinion and preference of the DM. They can and must be taken into account, but not at the beginning, altering reliable data with artificial weights.

The DM must act when he gets a result based on reliable data, without human intervention. Then, he can use his expertise, knowledge, reasoning, and research, to amend the solution or even reject it, but with reasons and facts.

The large difference is that in so doing the DM may have information related to the mathematical solution found by a MCDM method, that may be exogenous, that he did not have at the beginning of the process,

For instance, if the solution indicates that alternative A1 is the best, it certainly is from the mathematical point of view, but not perhaps when analyzed with the environment where it applies. It could very well be that the DM realizes, only at that moment, that A1 is very sensitive say to international prices, and that these have a history of large variations and up and downs.

The DM may consider that it is too risky, and opt by the second-best alternative.

Therefore, the definitive solution is reached by the DM helped by the MCDM method. There is another advantage to this bottom-up procedure, and it is the fact that a final result and decision, is obtained by a DM, supported by real aspects. Observe that in our systems, it is assumed, without any foundation, that what is in the mind of the DM, applies to the real-life project.

I hope my comments can help

Nolberto Munier