Dear Mr. Won Chol Yang and coauthors

Reference is made to your article:

“Materials selection method using improved TOPSIS without rank reversal based on linear max-min normalization with absolute maximum and minimum values”

I read it, and here are my comments:

On page 2 you say “Kong mentioned that the vector normalization as the reason of the rank reversal and the normalization must be independent of the alternatives [18]”

I concur partially with this statement, because I don’t think that normalization produces RR. Now, how normalization must be independent of the alternatives if precisely it works with their values?

Just let’s analyze TOPSIS very rational structure.

1- The initial decision matrix gives the performance values and the corresponding actions for each criterion, i.e., maximize or minimize.

2. If we use the sum of all performance values in a criterion i.e., the ratio between each aijand 📷 ∀j, we will get for each criterion its normalized value, with the proportion between them holding.

3. We can multiply thus, each value of each criterion by the corresponding criterion weight, which of course, is equal to all of them.

4. If a criterion calls for maximization, we select its maximum value (the best), and its lowest value (the worse). If it calls for minimization, it is the opposite.

5. We find the difference between, each aij regarding the best and the worst, that is, we compute distances.

I don’t think this normalization has anything to do with RR, unless, perhaps if we use min-max normalization procedure. I have experimented with the same problem, subject to three different normalization processes and the ranking does not change except for min-max.

Now, if we delete an alternative, this is a different history. The reason is that we are changing the initial decision matrix. We get a new one, which probably does not coincide with the original, and we know if it is a good or bad alternative considering its relative position in the ranking. However, if we add a certain alternative, we don’t know if it is good or bad, because we can’t analyze the multiples interrelationships and effects, and thus, the added alternative may be the best, the worse, or be somewhere in the ranking.

In may opinion, the reason for RR is that alternatives selection must be done independently and referred to a constant system, for instance to coordinate axis, like in Spotis, or analyzing each alternative separately and determining a value that is function of its contribution, like in SIMUS. In this last case, each alternative is computed based on costs of opportunity (that is, the cost of an opportunity not taken). Thus, the alternative that best improves the objective (max or minimization) is the chosen.

6- In formula 13, k = - 1/ln(n). I suggest to correct it.

7- Well, using Uk and Lk makes a lot of sense and it is a very attractive procedure, but I don’t understand how you manage them to be independent of the alternatives, since they are part of them, unless you equal Uk and Lk with arbitrary high and low values, and far from the original maximums and minimums. Interesting, and in my opinion, feasible. The problem, as I see it, is how you determine those high and low values for each criterion.

In Section 2.3 you say” This formula becomes the analytic expression for the sensitivity analysis to attribute weights”, and develops a complex formula for weights, to be used in sensitivity analysis (SA). However, in other part of the article you say that you use entropic derived weights. Could you explain it?

In my opinion, and contrary to what all MCDM methods, do, weights can’t be used in SA (except entropy weights) or statistical, because they are a measure of criteria relative importance, but not adequate to evaluate alternatives (Shannon’s Theorem), that establishes that the importance of a criterion depends on its discrimination.

8- You mention velocity of change of the alternative when a criterion changes, which for me is a concept that I have not seen before. However:

a) Are you assuming that all criteria changes produce changes in the alternatives? Normally, this is not the case, since very often, only a little number of criteria affect the alternatives, albeit all must enter in the computation. The criteria components of this subset are called with reason, binding criteria. The others are irrelevant, in the sense that their changes do not affect the alternatives.

b) You are assuming that you can increase/decrease the value of a criterion indefinitely. Normally this is not the case, and there could even exist binding criteria that cannot accept any variation, and thus, making the solution very sensitive.

9- You say: “The attribute with largest value of Sk is the most sensitive attribute”

I don‘t hink that speed is connected with sensitivity. What is connected, is how much s a criterion allowed to change.

Anyway, these are my comments that I hope can help you

Regards

Nolberto Munier