Dear Wojcieh Salabun and coauthors

I read your paper

How Do the Criteria Affect Sustainable Supplier Evaluation? - A Case Study Using Multi-Criteria Decision Analysis Methods in a Fuzzy Environment

And these are my comments:

1- Unfortunatelly, very scant information on the scenario is given. The paper only informs that it is related to batteries, give the number of suppliers and say that there are 15 criteria, but don’t say which are they, and give the labels of five sectors or clusters. It only informs that refers to batteries suppliers for swapping stations. And what are swapping stations? As you understand, the reader does not have the obligation to know about them.

2- On page 10 you say: “The resulting ranking was considered as a reference point in the study, with the ranking order of the options presented in Table 1”. I understand that there is a mistake here, since it should be `Table 3’.

3. In section 4,1. You say “A sensitivity analysis also provides more comprehensive knowledge and a greater view of the overall problem, showing the decision-makers what might change in the results under changing external conditions”

This is in my opinion, an excellent contribution to sensitivity analysis (SA) definition and properties. Its merit is that in most cases it is the reason by which a DM can reverse the best alternative and select the second one. Unfortunatelly, this is very rarely mentioned in SA analysis, which relies only on the existent criteria.

However. I disagree with your sentence “Therefore, the researchers adopted an approach in which the weight of each criterion was modified at +/- 20% from the initial value”

I disagree, because you can’t assume that all intervening criteria may change +/- 20%. This is not realistic, since each intervening or binding criterion, that is, that conforms a certain alternative, has its own allowed range of variation and even can have none. In addition, it appears that all criteria are binding, which is very seldom the case, and thus, it could be that only six or seven criteria, out of the 15, are relevant.

4- The paper considers excluding criteria to compute the ranking. I think that this procedure may be incorrect. One thing is to consider irrelevant criteria, determined after a solution is reached, and another, not considering them from the beginning, and solving a problem that ignores criteria, which although irrelevant according to entropy, are needed. Entropy, or better, its complement, information from entropy, tell us which are the most important criteria to evaluate alternatives, but they don’t indicate that some of the others can be eliminated because have a high entropy. They contain information, perhaps very little, but information that it is not advisable to ignore.

Strangely enough, you determine that the most important criterion is C2 or Transportation cost, and you decide to eliminate it?

5- I am curious on something. I guess that batteries are for car factories or for retail. You consider transportation distances, that oscillate between 1055 km between Beijing and Wuhan, to 167 km between Beijing and Baoding, and 926 km between Wuhan and Baoding, but in my opinion, this means nothing if you don’t specify the destination of the batteries that can be manufactured in each of the three places. Obviously, if they are to be used in the same city where they are manufactured, the transportation cost is not very important, but it could extremely important if the distance between origin and destination is high.

You say: “𝐶2 (0.750, 0.857, 1.000) (0.167, 0.200, 0.250) (0.500, 0.600, 0.750) (0.750, 0.857, 1.000)”

This illustrates that from transportation you have three values for each option. But what do they mean?

Of course, it is understood that they indicate in TFN the smallest likable value, the largest possible value and the most probable. But of what? In the case of transportation cost what the refer to? Cost of unit/km?, and in case of distance? As far as I know distances are fixed, unless there are several routes between two places. If they are, why do you need to use TFN?

If there is a manufacturing site, it can be understood in the sense that there a minimum cost of transportation for say train, an upper for say truck, and middle say considering another route, but 0.075 may be a percentage of what? The values between options are quite similar, suggesting that distance is not an issue, what is it then?

6- You assume that only 8 criteria are to be considered, out of 15, i.e., those are the criteria that participate in the selection of the ranking, which for me is a very correct, and unfortunately very seldom done in papers published, where it is assumed that all criteria participate. Now, how did you select the 8 criteria? On what basis?

However, in my opinion, the quantity of criteria that are relevant, in your case, 8, can’t be considered that apply to all alternatives. My research in many cases, constantly shows that the number and the type of criteria is particular for each alternative, and thus, it does not apply to them all in the same set of criteria, although, in general, there are always some criteria that repeat in each alternative, naturally, on the same problem. That is, for A1 they may be C9, C2 and C7. For A2, C2, C5, C7 C10, C15 and C4. For A3, there could be C7, C9, C1, etc., therefore, I don’t think that you van speak of the same set of criteria for all alternatives.

You say “The other criteria did not affect the ranking order of the options”

I agree, provided that in SA you refer to evaluating ONE alternative of the ranking, not all of them jointly.

7- In reality you don’t need to use fuzzy. If you use triangular numbers, which of course is correct, you can use for each type of criterion, two criteria, one for minimizing the lower value (no less than), and another for maximizing the upper value (no more than). In this way, the final value will be computed by the software, and most important, considering their interaction with all other criteria that are using the same resource, for instance money. As un example, if you have a minimum and maximum value for storage, the software will find the INTERMEDIATE value that also satisfies another criterion, for instance, funds to fabricate a product according to demand. Naturally, I am referring to Mathematical Programming.

I hope that these comments are considered useful.

Best regards.

Nolberto Munier