# 198

Dear Bartłomiej Kizielewicz, Tomasz Tomczyk, Michal Gandor, Wojciech Sałabun

I read your paper:

Subjective weight determination methods in multi-criteria decision-making: a systematic review

My comments:

1- Page 3 you say”…. such as pairwise comparison of criteria, evaluation of

criteria against alternatives, or scoring. Based on their experience and knowledge”

I don’t think that you can talk on experience and knowledge using pair-wise comparisons, since it is a matter of feelings

Comparing criteria with this procedure the DM simply assigns a ratio, that is, a quantitative value based on the DM intuition. This is only a set of wishes without any mathematical support. There is no reasoning, no research, no analysis, no nothing, onlya value which, by the way, can be absurd, like saying for instance that maintenance is 3 times more important than safety in evaluating projects, and a value that can changed next day according to the mood of the DM.

It is legitimate to compare two compare two criteria; what is illogical is to assign a value to that relationship. For instance, how can the DM compare subjective criteria, like tenderness and love, and give a value for the preference?

I have been working in MCDM for the last 30 years, and I still cannot understand how this illogical comparison still takes place, especially, when a myriad of researchers have rejected it.

It is of course only my opinion, and I would be happy if somebody can explain me its rationality.

It is paramount of course to take advantage of the know-how an experience of the DM, but not trusting in what he believes or feel, at least in serious projects. It is also essential to quantify the relative importance of each criterion, no doubt about it, but using this method, against any rational thinking? Where is the logic?

2- “Because they can structure complex decision-making problems”

You refer to AHP and in my opinion this is inexact. Precisely due to its lineal hierarchical structure the method is unable to solve not even medium complex problems. The reasons?

a) Using pair-wise comparisons and assigning weights does not have any mathematical or common-sense support. However, it can be used in simple personal problems where the problem is related to the DM, like selecting a movie to watch or a restaurant to dine. But the DM can’t apply it to large projects that involve thousands of people.

This is what Arrow in his ‘Incompatibility Theorem’, calls ‘dictatorship”, because nobody can vote for others, and this is exactly what AHP does. This is a well-known theorem, however, users of AHP remain silent as also remain silent on many other aspects of the method. WHY?

b) Since AHP only accepts independent criteria, it cannot be used in problems where criteria are related, as happens probably in the 99% of the real-life scenarios. The method is not to be blamed for this, because it was built in this way. It is people that are using a method that is not appropriate for their problems.

c) AHP demands that the initial matrix must be transitive, and if not, demands to correct it, what normally is almost impossible and unnecessary in complex problems to comply with this requirement, which in addition does not have any non-sense. Why a DM can’t be inconsistent? Who said that? Ans especially, on what grounds that restriction is imposed?

d) AHP assumes that what is the mind of the DM can apply, as by a decree, to the real-world. This is completely illogical from any point of view and whatever the reasoning, and Saaty himself wrote about it, when saying that this may or may be not the truth. It is also what Arrow says, since the DM is forcing the real-world to accept what he thinks

For years I have mentioned these aspects many times in RG, papers, conferences and books, but surprisingly nobody in 10 years of my participation in ResearchGate has denied or rebutted what I say. Why?

Because there are no valid arguments to support what the AHP method proposes.

With due respect, I wonder why thousands of people continue using this method, and still worse, researchers trying to “improve” it in hundreds of papers, by applying fuzzy, or discussing of preferences or analyzing inconsistencies. In my opinion, there is a trend to being blind to the whole picture by analyzing details. The whole is that the method is faulty and flawed.

In my opinion, the only reason for its wide acceptance , at least for practitioners and students, is due to the easiness of the method. The user just put what is in his mind or feeling, press the start button and voila! , gets the result, provided that a formula does not force him to change his estimates.

Sincerely, Dr. Kizielewicz, where is rationality or at least common sense in this procedure? Where is the mathematics here? Why to spend time by trying to improve something, that probably was right at its conception, since most industries, about 1950, followed

the lineal hierarchical structure, centuries old, but not longer valid in the 70s or 80s, let alone these days, when most firms adopted the network organization structure, with

multiples relationships in any direction. Even Saaty, assumed the networking by creating the ANP.

I have read hundreds of articles using AHP, and I am not judging them, because nobody appointed me as a judge. I only try to understand why this method is still used. It looks that the work of Roy, Brands, Hwang & Yang, Opricovic, that created probably imperfect but rational and thought methods, like SAW, PROMETHEE, ELECTRE, TOPSIS, VIKOR and many others, following a different way, do not have the popularity of AHP.

I guess that these methods demand reasoning, thinking, consulting, experience, know-how, analyzing, something that AHP does not ‘necessitates’, for with feelings it is enough….

If possible, I would very much appreciate your answer, either public or private ([email protected])

3- “Methods based on linear programming are advanced tools in Multi-Criteria Decision-Making, enabling precise and optimal determination of criteria weights. Thanks to its mathematical basis, linear programming ensures consistency and accuracy in the decision-making process, which is particularly important in contexts requiring high precision

and minimization of subjective error. Using linear models for determining criteria weights allows for unambiguous results that reflect the actual importance of individual criteria, which is crucial for making informed and accurate decisions”.

Precise and optimal? Both are unattainable in any MCDM method

You are right regarding LP, but not on “minimization of subjective error.” LP, does not minimize subjective errors, they are not even introduced in the method. What it does is to minimize costs, pollution, water consumption etc., or maximize IRR, production or benefits looking for a balance, a compromise solution, not an optimal

What you say about LP quantifying criteria weights is true, but unfortunately, criteria weights are useless to evaluate alternatives (Shannon’s Theorem).

When you apply LP to a decision matrix you get the best ranking of projects, and at the same time the marginal utility values for only the criteria involved in the selection of the best alternative. Those utility or marginal values can in a sense, rank criteria relatively

4- “ Within methods based on linear programming, there are several widespread approaches, such as BestWorst Method (BWM), FUll COnsistency Method (FUCOM ……)”

As per my understanding the only MCDM using LP are Goal Programming and SIMUS

5- “However, all these approaches share a common feature - the desire to optimize decision-making processes by precisely determining criteria weights using linear programming.”

I believe that you are mistaken.

These are my comments. I hope they can help

Nolberto Munier