# 118

Dear Mahmut Baydas , Mustafa Kavacık , Zhiyuan Wang

I read your paper:

Does the Performance of MCDM Rankings Increase as Sensitivity Decreases? Graphics Card Selection and Pattern Discovery Using the PROBID Method

My comments:

1. This is a really an intriguing and complex subject, however, it is not clear if your article refers to the typical sensitivity Analysis (SA), which tries to find the strength of the best alternative - and the others if the DM wants - regarding to variations in some criteria, or if it also refers to the performance values.

What is the meaning of ‘Performance Rankings’?

I guess that it refers to how strong the best alternative or option is, when there are variations in the criteria on which it depends. Sensitivity, in a certain problem is fixed and subject to he allowable variations of the criteria the best alternative depends on. That is, if alternative A depends on criteria C4, the strength or degree of sensitivity of A is determined in the solution, since it a function of how much can decrease or increase C4 be without perturbing A. That is it depends on the range of variation of the corresponding criterion.

Suppose that C4 has zero variation, that is, it cannot be increased or decreased. In this case A is very sensitive, because a very little variation of C4 removes A from the first position. As a matter of fact, the variation for every criterion must be computed by the method.

In essence, in analysing SA it is necessary to consider:

a) The best alternative and the ranking. Each alternative can be analyzed indepently

b) The best alternative should be selected as a function of its weighted scores (not related to subjective weights, but to the number of criteria it satisfies)

c) Each alternative is subject to a set of criteria used for its evaluation. It is true that all criteria participate in the evaluation, but not all of them are responsible for the selection of each alternative. Thus, we can have 4 alternatives and say 9 criteria. Assume that the best alternative is A3. In selecting A3 only some criteria participate, say C1, C5 and C9. These three criteria are the only significant, the other six are irrelevant.

d) Each of these criteria has a particular range of variation, related with the selected alternative. It is this variation in each participant criterion that defines sensitivity, of the alternative.

2. In the abstract you state “As in other techniques, approaches, and methodologies, if the results are excessively affected when the input parameters change in MCDM methods, this situation is identified with sensitivity analyses”

This is true, but incomplete; the SA will determine in any case if the solution found is strong or weak

3- You say “Observing the holistic change of all alternatives compared to a single alternative provides the researcher with more reliable and generalizing evidence, information, or assumptions about the degree of sensitivity of the system”

I plenty agree with this statement. Some scenarios are so sensitivity, whatever the alternative sleeted, that it is really risky to proceed with the project. But of course, it also depends of the nature of the criterion. If a criterion has low variation, but many years of data shows that it remains with the same value, the risk in accepting ii is low. Other criterion, like an international price of soybean for instance is heavily fluctuating, and thus, it has to have an allowable variation for the corresponding alternative being selected.

4- I do not understand how you can define a fixed point to measure sensitivity. It is not a metric, there is not a number for it, but an indication that the alternative is dependent to the characteristics and performance of criteria, as exemplified above.

In my opinion sensitivity does not have a value, you cannot measure it. Based on what?

In addition, since normally an alternative depends on different criteria, their variations are different, and thus, in a system, you may have, even for the best alternative, that it has different sensitivities regarding the different criteria. It may have good sensitive to criteria C9, acceptable to C3, and zero sensitivity wit C7. That, is it is strong regarding C9, regular with C3 and extremelly weak regarding C7. How can you compare the three of them, that are intervals, with a fixed point

The DM must study the nature of each criterion, and act in consequence. If C3 and C7 are not very important, while C7 is very important, the alternative is very weak. Importance does not mean their subjective weights, which are irrelevant, importance is measured by the impact that each criterion has on the respective alternative. For instance, in a site selection scenario the best alternative is A5, and one of the criteria it depends is “Social unrest’. If the country, represented by A5 has continuous fights with trades, unions, and earnings repatriation, it is a very important issue to consider, even more important that a criterion like “Total cost”

4- “sensitivity of an MCDM method is high’

I do not think you can generalize

5.” In short, uncontrolled hypersensitivity disrupts not only the ranking but also external relations, as expected”

What do you mean with this?

6. “MCDM. However, it is not clear whether the determining factor of sensitivity is the weight coefficient of an MCDM method’

Of course it is not. Weights only measure criteria relative importance and are not related to evaluation.

7. “We suggest that the change or sensitivity in the rankings can only be measured accurately by comparing them with a fixed reference ranking”

And thus, completely ignoring the nature and relationships between criteria

8. “For example, “price” for a computer graphics card and “GDP per capita” for a country’s economic performance can be a fair reference point. This is a reasonable choice because we can predict that as a result of competition, there should be a close relationship between performance and price.

Sorry. I do not see any rationality in this.

In this study, we focused on the discovery of determinants of the degree of sensitivity of MCDM methods through data analytics

Doing SA you can do precisely that, but not from data analytics, but from MCDM results

9. In page 8 “As it is known, “sensitivity analysis” is frequently used in the evaluation of MCDM methods”.

Not in my book. SA is used to determine the strength of alternatives after they have been evaluated by one of the many MCDM methods

10. Page 9 “According to Table 3, it is understood that under conditions where sensitivity is high, the relationship with price decreases and vice versa”

As far as I know the sensitivity does not change, it is determined by Linear Algebra. It determines that sensitivity values computed by certain MCDM methods and according to data. Reasoning, without formulas, I do not see that said relationship exists. It is only a warning to the DM, making him aware of the fragility of the solution found.

As an example, if you have to take a train, which departure time has been set by the railway, and you are far away from the train station, taking the train on time is very sensitive to the distance from your house, your car speed, existing traffic, rain, etc. i.e. to your criteria. Say that you leave home early and have plenty of time to catch your train, however you did not count that at that time is when the car traffic is heaviest, adn so heavy that the original allowance you had, no longer exists.

11. In page 9 - You mention a basic equation in MCDM. Could you tell me please which is that equation? I never heard about it.

These are some of my comments. It would be nice if we can discuss them, since, in my humble opinion, your method reaches conclusions that for me are unreal

Nolberto Munier