Dear Irik Mukhametzyanov and Dragan Pamucar

I have read your paper

Sensitivity analysis in MCDM problems: A statistical approach

My comments:

On page 3 you say “Consequentially, the alternative choice does not depend solely on the criteria that one uses to evaluate those alternatives but on the MCDMM that one uses as well”

In my opinion, the alternative choice depends on the criteria, since if we use the same initial matrix, aim at the same objective and use mathematical algorithms, the result should be the same, i.e., regardless the method used. The issue that we get different results, using different methods and with the same data, invalidates that assertion of dependency on the MCDM method.

“These procedures calculate, for a given pair of alternatives, the best alternative, the closest set of weights that equates their ranking”

Please, illustrate me, because I don’t understand how you can use entropy in sensitivity analysis (SA).

SA means increasing or decreasing a criterion importance, but you can’t increase or decrease the entropy value of a criterion, because it depends on the discrimination of its values. Of course, you can modify one or two of its values and even doing that, the entropy may not change, although it can affect the alternatives.

“These procedures calculate, for a given pair of alternatives, the best alternative, the closest set of weights that equates their ranking”

Sorry, I don’t understand what it means. Which rankings do you want to equate?

“the existence of dominance makes the sensitivity analysis almost unnecessary.”

This is new for me. Why dominance makes unnecessary SA? Both concepts are not related. In SA we are not working with alternatives, but with criteria, that can change the ranking of the alternatives

“is approach is based on the geometric characteristics of optimal decision regions in the probability space”

I don’t think that there exists an optimal decision region. The decision region contains all feasible solutions of a problem, and the optimal is only found in some of its vertices, and there is a theorem that demonstrates this

“Also, in Triantaphyllou (1992) the sensitivity analysis approach is described for a class of inventory models”

And I agree with him, because SA depends on the capacity of a criterion to change without affecting the best alternative. And that capacity, that measures the allowed increase or decease may be considered an inventory for that criterion

In page 4 “However, the fact that there are multiple methods that recommend the same choice is not a satisfactory warranty of rationality and quality of the calculated solution (Pavličić, 1997”

I plenty agree, and for this reason I don’t see which is the utility in solving a problem by different methods. Where is the gain? What conclusion can be extracted?

“the analysis is often based on an appropriate sensitivity analysis of the results to changes of certain parameters in the decision-making model (Yu et al. (2012); Stevens-Navarro et al. (2012); Li et al. (2013a); Li et al. (2013b); Corrente et al. (2014); Kannan et al. (2014)).”

This is quite reasonable, but how to identify the parameters? By the way, they have a name ‘Binding criterion’. Unfortunatelly, that parameter is identified as a criterion with the maximum weight, which may be certainly intuitive, but that do not have the minimum mathematical support.

I could add, that sensitivity analysis can be measured by studying the impact that external, but expected issues, can have. For instance, if the best alternative depends on a criterion that have large fluctuations, like stocks price, obviously, the best alternative is not stable, and very risky.

Everybody can check this.

Consequently, it is very important the determination of the binding criteria, that is, the criteria that are responsible for the best alternative selection, and discarding the others.

How many MCDM identify the binding criteria? None, except Linear Programming.

Consequently, in many cases practitioners are changing criteria that are completely irrelevant for the best alternative.

In my opinion, SA is not well understood for many practitioners

In page 4 “As specified in the shown research studies, the selection of an optimal MCDMM is a very complex problem which without any prior sensitivity analysis of the solution can have a wrong selection”

SA is a post result analysis; therefore, how can you make a pre assessment of the results?

“This article presents a study of estimating the variation of alternatives according to the criteria for the results of ranking alternatives, and in connection with this, the approach to improving the reliability of decision-making”

It appears that you are contradicting yourself. First, you say that you need and ante result,and now you speak about a post result! The latter is not a novelty, it is the essence of SA since decades

Page 5 “The reason for this is the fundamental uncertainty of nature. The correct wording shows how accurately the alternative is evaluated by the criterion”

I don’t think that this is entirety correct. If a criterion is the existing road distance between A and B, where is the uncertainty? However, certainly there could be lot of uncertainty on nature

“As specified in the shown research studies, the selection of an optimal MCDMM is a very complex problem which without any prior sensitivity analysis of the solution can have a wrong selection”

Alternatives are given by the stakeholders and owners of a project, MCDM has nothing to do with their identification. They even existed prior to the selection of any MCDM method, therefore, it is irrelevant if they are or not significant for the DM; I am curious and don’t understand why you bring this issue here.

Just a simple example. You have to select a restaurant for dinner and have six options. The restaurants are already there and may be significant for their owners, otherwise they wouldn’t be in business, therefore, those alternatives (the restaurants) are not to be found, but given.

I believe that there is something missing in your analysis, and its is that you are using increments / decrements of criteria without considering if they can increase /decrease.

Criteria cannot increase or decrease, infinitely, because they have limits, which in many cases depend on other criteria. This is the reason by which in SA you can’t consider criteria changes independently, but their joint variation. In other words, ceteris paribus principle does not apply here.

As an example, if you are measuring the performance of a car, you cannot consider only the changes in speed, because the change of speed is related to fuel consumption, the strength of the wind, which in turn is related to the aerodynamics of the vehicle. The whole and holistic effects is what define the performance.

It is the same in MCDM.

In page 27 “Following the obtained results, the evaluation of alternatives according to the criteria and the choice of the criterion for ranking alternatives using different ranks have a profound effect on the final choice”

Sorry, I don’t understand this paragraph. The first part is correct, but what does the second mean?

Which ranks you choose?

I hope these comments may help you

NOLBERTO MUNIER