# 186

Dear BARTŁOMIEJ KIZIELEWICZ, ANDRII SHEKHOVTSOV, JAKUB WIĘCKOWSK, JAROSŁAW WĄTRÓBSKI, and WOJCIECH SAŁABUN

I read your paper:

The Compromise-COMET method for identifying an adaptive multi-criteria decision model

Dear authors:

I make my comments along with a first reading of a manuscript. In this case, and based on what you say in page 3 “Motivation: The principal motivation of this paper is to propose a method to identify adaptive decision models. Existing methods so far are susceptible to the rank-reversal paradox”

Consequently, I assumed that you were referring to what is known as Rank Reversal (RR) in MCDM literature, that is, the change in activities rankings when a new alternatives is added or delated, which is not what you did, that is, the change in ranking when the matrix is altered, but keeping the same number of alternatives, something that also happens in sensitivity analysis

If I may, I would suggest making clear what type of RR you are referring to, that is, Changing the number of alternatives, changing vectors in the matrix, or SA

My comments:

1- Abstract “However, the choice of normalization technique significantly influences the final ranking. Different rankings are obtained using different normalization techniques for the same alternatives and methods. At the same time, the rank-reversal phenomenon in observed in many popular MCDM methods”

In my opinion, RR is never a phenomenon or a paradox:

In changing the number of alternatives, it is due to geometrical reasons.

In switching alternatives vectors, it is due the new interrelationships between the original matrix without an alternative and the new matrix with a new alternative vector.

In SA it is due to the fact that the allowed variation of a criterion was overpassed.

In the three cases RR is neither a phenomenon nor a paradox, it is simply a consequence of matrix operations.

2- I don’t think that you can consider sensitivity analysis as a complementary technique.

As a fact resolving a MCDM problem without a SA isa waste of time, because the DM never knows if the result is feasible or realistic, considering the direct influence of some criteria.

3- Page 3 “The paper presents the C-COMET method, offering a unique approach to establish adaptive decision models impervious to the Rank Reversal Paradox. This fills a critical gap in MCDA, providing a coherent and adapt able decision-making framework even in the presence of changing alternatives”

I doubt that COMET is impervious to RR, maybe it is impervious to different normalization

There is not a gap in MCDM since RR is unavoidable

4- In page 5 you name a set of MCDM methods that are immune to RR, among them SIMUS.

I am afraid that you are mistaken, for SIMUS is also subject to RR, albeit is much more resistant than other methods to it. It is due to its algebraic properties that other methods do not have, mainly, that it works in spaces not with lines, (basic Linear Programming), but as should be, and reinforcing my theory, it is also subject to RR. I will be happy to share this information with anybody, that anyway will be published shortly, I hope. What appears to be immune, as per my tests is in preserving the alternatives ranking when comparing results with Sum, Maximum value, max-min and vector normalization.

5- Page 9 “Normalization methods are also used to eliminate preset units of criterion functions”

What does this mean?

6 - “The effectiveness of the MAIRCA method hinges on identifying the gap between ideal and actual weights”

Interesting, and how does it determine the ideal weight?

“The alternative with the smallest total gap value is the closest on the ideal weights across the most criteria”

And where this assertion comes from or is it only an assumption?

7- “The Characteristic Objects Method (COMET) is one of the MCDA methods that is characterized by complete resistance to the Rank Reversal Paradox”

Audacious assertion that I guess will be explained. Figure 5 does not explain anything

8- “Notice how several alternatives get a higher position in the two first columns because we add A1 and remove A2”

In so doing, you are preserving the dimensional space, consequently the problem does not change dimensions, that is the cause for RR. Why don’t you try adding a new alternative each one without removing any other?

Of course, eliminating an alternative and adding a new one may give different rankings because you are considering the same problem with different vectors and fundamentally because the slopes of the original criteria have changed in that replacement. But this is not related to RR but to a matrix that is different to a former matrix, but with the same n umber of activities

9 - “This approach provides high stability and consistency, and due to its use of the COMET method, it warded off the Rank Reversal Paradox”

Where is the paradox? I do not see any contradiction

What I do not understand is your approach to this subject which its objective is to demonstrate that COMET is immune to RR, but you develop a complex procedure switching activities. Of course, that the could be changes in the ranking, but this is not RR, as least as MCDM

These are my comments, hope they can help

Nolberto Munier