# 211

Dear BARTŁOMIEJ KIZIELEWICZ, JAKUB WIĘCKOWSKI, BOGDAN FRANCZYK, JAROSŁAW WĄTRÓBSKI, and WOJCIECH SAŁABUN

I read your paper

Comparative analysis of re-identification methods of multi-criteria decision analysis models

My comments:

1- Abstract. What do you mean by reidentification of models in MCDM?

2- “Addressing the challenge of re-identifying decision models brings up issues related to updating the last version of models to preserve their effectiveness,particularly in nonlinear decision scenarios.”

Yes, you can improve an existing MCDM model introducing some features, however, it you need to modify its structure because it could not treat some problems, it means that the original method was not effective. If in the past you couldn’t t model a problem properly, as happenned in all MCDM methods, they are not effective. You can add some cosmetic changes like using fuzzy, but if the method was unable since its conception, to reflect a reality, using fuzzy is not a remedy.

Look at thermodynamic models, for instance, or even the gravity theory, or the relativity theory. Most of them enounced centuries ago, and that did not change, and are as useful as the were at their conception. ANP is a good example, it was developed to correct the assumptions in AHP by considering criteria independency, and as that unable to model real scenarios. Linear Programming is another, developed in 1939 it could efficiently solve problems with moly one objective and with quantitative criteria, therefore, even when they are still very useful in certain type of problems, it is necessary to recognize that it can’t of solve most present-day scenarios, because structurally it was not designed for that. This is the reason that SMUS appeared, strongly based on LP but with a different structure, that can handle simultaneously up to 100 different objectives in any mix of qualitative and quantitative criteria.

3- “ These methods were evaluated against a benchmark comprising four selected MCDA techniques”

Do you think that a high correlation between the rankings obtained by different methods is a benchmark? On what grounds is your assertion based? That is, how correlation between these rankings represents reality? You even confirmed this assumption is rather useless when you say “providing benchmarks for selected methods, the practical implications of such comparisons raise critical questions”, so it is not only my opinion, it is only an assumption that nobody could yet justify; why then, is it used? This is something that I never could understand, however, why is it used? Due to a very simple reason: Nobody knows how reality is; if we knew, we wouldn’t need MCDM! So, everything is accepted as permissible.

4- Page 2. “The re-identification process is driven by stochastic weight search for the TOPSIS, VIKOR, and SPOTIS models”

Yes, you can, but what for, if criteria subjective weights do not play a role in alternatives evaluation? Of course, you know that if they were they would be contradicting Shannon’s entropy theorem. So why to waste time on subjective weights? Why not to use entropy weights that al least have a solid foundation? On course, DM opinion, experience and know-how is very very valuable when applied at the right time, that is not at the beginning by modifying real data by using invented weights, but at the end, when he has a result based on solid data, even with some uncertainties.

This result may be studied and corrected if necessary, or even rejected, and where it is acceptable for the DM to weight some criteria, not by intuition, but after research, investigation, discussions, etc. He can run the software again with his/her modification and analyze and compare results, which is his function. He can also have a solid justification to the stakeholders when he must submit his conclusion. Don’t you think that this is a more reasonable approach?

5- Page2 “there is a clear need for methods to adapt and re-identify existing models under more complex, real-world conditions.

Well perhaps you could explain why a method like SIMUS has been used without any modification or needing any adaptation since 2014. It is using the same Visual Basic version since then. Of course, it needs some cometic changes, but not structural changes.

Page 3 “In this case, the ideal solution represents the best possible outcome for each criterion”

You said that: “for each criterion”, but the solution of the problem is not the sum of each criterion solution. This solution is reached considering the intersection between all possible criteria, before computing the solution of each one, and this unfortunately, is something that the more than 200 MCDM methods do not consider except Linear Programming and Goal Programming.

Remember that in may aspects of life and scenarios the result is not always the sum of the parts. In my opinion, until methods continue not respecting this elemental concept, any modification is only cosmetic. Of course I refer to all present-day procedures ib general, I am not addressing your development.

6- In page 5 you say that SPOTIS is immune to RR. It is true that the method, fixing the frame independently of the alternatives is more resistant to RR, but as far as I know, it is not immune to it, because RR does not dependent on a method, any method, but in something that is a geometrical and logical consequence, due to the change of coordinate basis of the decision matrix, due to an alternative increase or decrease. The problem in dimension 2D is not the same in project 3D, or in 5D

7- “Overall, while linear models remain valuable for more straightforward decision contexts, the growing complexity of real-world problems necessitates the development of more advanced, non-linear approaches like SVR-COMET”

It appears that you ignore that linear methods can also handle non-lineal relationships.

You have for instance a product unit price from 3 different up to a certain demand in a single criterion C1.

Same for a higher demand in C2 and in C3 even a higher demand. That is unit prices depend on quantities bought, the higher the lower the unit price

Therefore, you can represent by linear equations corresponding to the diverse demands, a non-lineal situation and you can repeat this procedure for many different products and different demands in each one, without using weights

Of course, you will need to increase the number of criteria, which will increase computer time

8- Page 5. You speak about reference models as if they were yardsticks when in reality are MCDM methods, most of them affected by subjective weights that also do not have any mathematical support

9- You compare between SITW results with the reference models. Sincerely, I do not understand the purpose of this comparison and its advantage. You also speak about detecting non-lineal problems and that is important. However using LP it is detected automatically when instead of gi giving criteria shadow pieces it shows a Lagrange operator

These are my comments

Nolberto Munier