# 190

Dear Adil Baykasoglu, Elif Ercan

I read your paper

Analysis of rank reversal problems in ‘‘Weighted Aggregated Sum Product Assessment’’ method

My comments

1- In the abstract you say “we show that rank reversal problems also exist in WASPAS when classical normalization techniques are utilized. We also show through extensive computational experiments by using different problem instances that rank reversal problems can be avoided in WASPAS when modified Max and Max–Min normalization techniques are used”

I have been for years researching on rank reversal (RR), and found that it is unavoidable, at random, and existsin all MCDM method, and can prove this, and conclude that it is a feature of Geometry, as Gravity is a feature of Nature. Of course, I refer RR as it is known in MCDM and intrinsically related on adding or deleting alternatives. However, in despite that you define RR correctly in several places, in further reading it appears that for you RR is also produced by changing the values in the initial matrix, that certainly can produce changes in the rankings, but this is NOT RR. It is simply an exercise that verifies that if you change some values in the matrix, there will be changes in the rankings, which is natural.

2- You mention several times the ‘dynamic process’, verry important indeed, but not related with what you claim.

Definition of dynamic MCDM: “Therefore, this study integrates system dynamics with an MCDM method to enable the sustainability assessment by capturing the time-induced dynamic changes affecting long time sustainability performance of buildings”

By Ann Francis and Albert Thomas - Smart and Sustainable Built Environment

A MCDM project is a system that can be dynamic or not, and the above definition applies to the first case when changes take place as time goes. An example is the Sustainable Development Gosals (SDG) (United Nations), that analyzes the performance of 17 sustainable goals subject to many different changes and in different continuous periods, for instance every five years. In a period ‘n’ these goals are affected in a cause-effect relationship and thus, including feedback, by what happened in period ‘n-1’

Another example is the long-term policy to reach zero CO2 by 2050, considering changes in alternatives as oil fired power plants being gradually replaced by renewables, including options that are still at laboratory scale. The results in period ‘n’ are in part due to actions taken at the end of period ‘n-1.

The result of these new actions feedback to ‘n-1’ and may indicate the goodness of the new measures taken. For instance, in period 2029-2034, progress in CO2 reduction may illustrate about the goodness of actions taken at the end of period 2024-2029

These measures adopted at the end of ‘n-1’ may indicate for instance, that the rate of reduction of the output of contaminated plants is not enough, due for instance to the increase in electricity demand expected in period ‘n’, related to the demand computed at the end of ‘n-2’.

This is dynamicity, that is, changing a system as a function of time,and by far much more complex than problems that can be solved by most of the actual M CDM, like WASPAS, TOPSIS, VIKOR and most others, all of them also unable to solve this problem.

As seen, this is a complex scenario and I do not see anything like that it in the methodology you propose, however you mention it 13 times

3- Page 2 “Since the number of alternatives can change over time in many real-life problems, the MADM method, which suffers from the RR problems, may not provide consistent results and can recommend a non optimal alternative as the best choice”

It is true that the number of alternatives can change over time, but not only in number, since existent alternatives may be replaced by others.

These can be seen for instance in energy transition where alternatives that produce large contamination MUST progressively replaced by renewables like Photo Voltaic and Wind, and this is happening right now. Therefore, both can change at the same time, number of alternatives and existent alternatives be replaced by others.

4- Page 2 “WPM does not suffer from the RR problem”

Is there any proof of this?

5- Page 4 “transitivity axiom. In the third test criterion, the rank of alternatives in the original problem and the rank combination of alternatives in the decomposed problem should be the same”

Agreed, but to decompose a problem is not RR, because you are not deleting or adding anything since you always are in the same dimensional space, for instance, with three alternatives you are in a 3D space. If you change values in the matrix, you remain in the 3D, and there is no reason for RR. Add a new alternative and you will not longer be in 3D but in 4D, and due to coordinate transformations the ranking may change.

6- Page 4 The method adds WSM and WPM, I am not saying that it is erroneous, but I wonder what is the logic or the reason for doing that? On what grounds WASPAS is better than WSM and WPM?

7- Page 5 “ If an irrelevant alternative is incorporated into or removed from the problem, the final ranking of the alternatives changes”

And on what grounds can be decided that an alternative is irrelevant not?

In addition, if the stakeholders decided, supported by multiple reasons and analysis, that an alternative is irrelevant, why add it in the decision matrix?

8- Page 9 “All of the considered normalization techniques caused rank reversal problems in the WASPAS method’

And nobody investigated the causes? One of them could be that not all normalization methods keep the distance between alternatives. For instance, min-max. I have examples using four different normalization methods, and there was no change.

I am afraid that you mix RR caused by adding or deleting alternatives and producing a change in the ranking, with changing some values within the decision-making matrix, which can cause variable rankings.

I have my own theory on RR, which establishes that RR is unavoidable and at random. Unavoidable, because it originates when adding an alternative we change spatial dimensions. If we have a 2D or two alternatives (x and y) problem, and say four criteria, that are represented by four straight lines, we can find their possible intersection. That point determines the scores of x and y (on the two coordinate axes), and if it exists, it is the optimal point. This may be represented as a square, with 4 vertices, where one of the vertices is the optimal point, again, in 2D.

If we add an alternative z, the problem changes, since now we are in 3D and the square has transformed into a cube with 8 vertices. We no longer have lines representing criteria but planes, that may intersect and possible determine a new intersection, and thus generating what is k own as RR.

This is simple geometry, and in my opinion the reason for RR.

RR is at random, because the existence of RR depends on de values of the new vector that belongs to the newly added alterative. Why?

Be cause the new values form a different set of criteria and thus changing the existing relationships between them. It is at random, because this new added vector may or may not change original ranking, everything depends on the new values of the added verctor

What you do is different. Youn change values within the same matrix, without change of dimensions, on you get or not different rankings, which is reasonable because you changed the original matrix, like in a sum or in a multiplication. You change values and you get different results. This is not RR

These are my comments that I hope m ay be of help

Nolberto Munier