Why not?

Of course, you can rank more than 100 alternatives. PM me if you need support.

Of course, the number of alternatives in the TOPSIS method is not limited and all of them are ranked according to the distance from the ideal solution.

Yes, you can run TOPSIS even for large alternatives.

TOPSIS is great for the selection not for the prioritization.

If you want to rank alternatives not just picking one of the up, use other methods such as SAW.

Dear Shervin

Priorization is normally related with criteria, and effectivelly, TOPSIS is unable to do that, like most of MCDM methods.

SAW is the most elemental MCDM method, and does not priorize eidther

I have used TOPSIS several times in the past to rank 150 alternatives. The higher the number of alternatives, the better TOPSIS measures. Because the TOPSIS method has an equation dependent on the ideal values of PIS and NIS. While other MCDM methods produce "rank reversal (RR)" due to normalization, TOPSIS also has the possibility of generating RR for different reasons. My advice to you is don't settle for the "vector normalization" technique, which is the classical normalization technique for TOPSIS. Also try alternatives like Max, Min-Max, Sum, Z-Score, and Logarithmic. If you want to improve TOPSIS, you may want to try alternative distances to the vector distance in the equation. If you ask what kind of method TOPSIS is, I think it depends on the problem and the data. But in general, TOPSIS is a reliable method based on distances and I think it can be said that it has a slightly higher performance than the others (higher than average).

You know that the SAW method is a simple weighted aggregation method. It is the most classical method. A non-normalization SAW is the most primitive form of MCDM. Its advantage is that it is still a method used in daily life. The disadvantage is the high compensatory rate. An alternative that has a high value in a criterion, that is, an alternative that invests a lot in a criterion, can always be the first. However, "outranking" methods such as PROMETHEE-2 may not allow this in the first place, that is, they may prevent a criterion from becoming overpowered.

Dear Mahmut

As usual, you post interesting points.

1- RR- Very little is known about Rank Reversal, and there are several teories about it, however, I fail to understand why normalizatiuon should be one of them, when it applies equally to all values. As far as I know, all normalization are transformations:

To a linear space, as in Sum, Largest value, Vector, and Max-Min,normalizations, which puts all data in the 0-1 range, and thus, considering absolute values

To a log space with using log normalization. In this case, there are relative values.

As an example: You want go purchase a car A valued in 15,000 Euros and also has in sight another car B for 22,000 Euros, that is, a difference of 7,000 Euros, which is a lot.This is an absolute transformation.

If you have in suight two houses, one costs 1,000,000 Euros and the other 1,000,7000,

The difference is negligible. This is relative transformation using log

2- Which are the reasons by which, according to you, TOPSIS may produce RR; of course, it does, but WHY? This question applies to all methods except SPOTIS. and LP (SIMUS), and in both cases, the reason is very well known

3- In my opinion, TOPSIS is one of the best methods, howevefr I believe that PROMETHEE is better. WHY?

Because the distance in TOPSIS is chosen arbitrarily. In PROMETHEE, there is reaso ning on every aspect; there is some subjectivity, but explained

4- SAW without normalization is a simple table that can't be used because all units of criteria may be different, and then, you cannot add them-up for each alternative

Dear Nolberto, For a common problem, when you try different normalization techniques for the same MCDM method (for example for 150 alternative 8 criteria) why are sometimes not all sorting results 100% the same? In other words, why do some types of normalization cause a different ordering to be produced?

The relationship of RR production with normalization is a topic that has already been claimed in the literature. It is a fact that both RR and normalization are about producing a different sort order.

PIS and NIS values ​​may also change when you add or remove alternatives for TOPSIS. This means that the whole calculation is done all over again and new ranking results are obtained.

Dear Nolberto,

For a common problem, when you try different normalization techniques for the same MCDM method (for example for 150 alternative 8 criteria) why are sometimes not all sorting results 100% the same? In other words, why do some types of normalization cause a different ordering to be produced?

NM – I don’t know, but I presume that it could be related to the method you use, and especially with the precision you ask. Considering the large number of alternatives; a little decimal difference can provoke RR.

The relationship of RR production with normalization is a topic that has already been claimed in the literature. It is a fact that both RR and normalization are about producing a different sort order.

NM- Yes, I know it; but, is it a fact? If it is fact, please demonstrate it, you know that am not convinced with only words.

PIS and NIS values ​​may also change when you add or remove alternatives for TOPSIS. This means that the whole calculation is done all over again and new ranking results are obtained.

NM- Yes, of course they change. That is the reason why SPOTIS does not produce RR, because it uses always the same values. How? Simply. The DM selects and PIS and NIS arbitrarily higher than the maximum according to data, and minimum lower that minimum from data. In this way, it does not matter what you add or delete, the frame of references is always the same.

Dear Nolberto I think you think the normalization choice is unimportant. Because they all do the same job, according to you, they are equivalent. So let's just use Min-Max (or Z-Score) for all MCDM methods and make our job easier. Really?

Dear Mahmut

Your appreciation is incorrect, I think that normalization is essential.

Without it, there is no sense in using a MCDM method.

You can use the method you want. If one of them makes the job, why do you need several methods?

In SIMUS, long time ago, I chose a problem and used 4 different normalization methods. (Vector, Sum, Maximum value, and Max/Min); the four results were identical, although the aij normalized values were of course, different. As usual, I can prove what I say, could you?

I know that normalization is essential. I have never claimed otherwise.

Thus, a research effort is essential for the selection of normalization in this case. There is a difference in approach between you and me here.

Dear Mahmut

I never said that you don't support normalization. My sentence only meant that I do, in all cases.

By the way, if I remember right, long time ago you said that normalization was not needed in TOPSIS. Am I mistaken? If I am, my apologies

Your second sentence is interesting.

What research do you have to do to select a normalization method?

I may have said that for TOPSIS, normalization is not required if the units are the same, which is true.

This problem (selection of normalization) is difficult to solve and it is not just a problem with MCDM. One of my studies, in which I propose a couple of key criteria, will be published soon on this topic.

You may also want to review the discussion I started on RG:

https://www.researchgate.net/post/Why_is_Min-Max_or_Z-Score_generally_preferred_for_Artificial_Intelligence_Machine_Learning

Mahmut

Even if the data for TOPSIS are of same units, something that I have never seen, they could be formed by large numbers and small numbers, for instance, milimiters and meters