# 213

Dear Do Duc Trung , Tran Van Dua

I read your paper:

Development of RAMDOE: A new method for rapidly ranking alternatives with supplementary options and considering changes in criteria values

My comments:

1- Page 1 “all excelling in identifying the optimal choice among alternatives”

I am afraid that you are quite benevolent when using the word ‘excelling’ because unfortunately it is not true. None of the more than 200 MCDM methods excel in anything, quite the opposite; most of them are no more than coarse simplifications of a problem, even less, finding optimal solutions, simply because they do not exist in MCDM. Why? Because it is impossible to have a maximum benefit and at the same time the minimum cost

2 “However, as the number of alternatives grows,the need for recalculations from scratch becomes evident, posing challenges, especially in urgent decision-making scenarios”

This is an unjustified assumption. A method is simply an algorithm that works equally with 2 or 100 alternatives, only that the computer time increases. There is no reason to think otherwise. What can change, and it does, is the modelling of the problems since it depends of the characteristics of the problem. What you possible refer to, is that problems may be very complex, however, most MCDM methods remain without structural changes since they were developed about 50 years ago, even using fuzzy since that time.

Therefore, the world in the 70s is not the world we live today, however, the same MCDM methods are still used. I am not saying that they are wrong, only that they are obsolete to treat our present needs, where technical, economics, transportation, government, social issues and environment are heavily intertwined in most problems.

3. “However, using traditional MCDM methods alone requires recalculating the entire process when the number of alternatives changes (due to additions or removals)”

Not necessarily, there are methods that work with different number of alternatives only adding or deleting an alternative to the existent matrix.

4- page 2 “with MCDM aims to construct a regression equation that reflects the relationship between the scores of alternatives and the criteria”

All methods work linking alternatives and criteria, because this is the essence of MCDM

5- “However, this study has not considered the casewhere the values of the criteria in the additional option fall out side the range of values of the criteria in the existing options”

When you add an alternative to and existent matrix, the performance values of the alternatives are preserved, what changes is the whole criterion importance, because now a new vector is added with the new alternative, and the number of values is thus different. Consequently, what changes is the evaluation capacity of criteria, since their individual discrimination may be different, and also different the quantity of information each criterion provides. Shannon theorem easily demonstrates this.

The additional option you refer to, changes the number of coefficients. If you had, two variables, x and y (2D space), each one with their coefficients, and you add variable Z, you will be in 3D space, and the number of coefficients raises from 2 to 3.

In adding new criteria, it is obvious that its range of values must be in agreement with the existing range, that depends on the number of alternatives

Page 2 “To address this limitation, this study proposes a solution to rank alternatives considering the adjustment of criterion values in the additional alternatives”

Please, remember that when you are adding a new alternative you are adding a vector, that has values for each criterion. For instance, in adding alternative z, and if there are a criterion like cost, you must put a value of the cost for that new alternative, if not, the alternative will hace al Cj = 0 for cost.

6- In page 6 you cannot consider only 5 alternatives out of 7 because in so doing you are partitioning a system. What happens, if for instance, A1 must precede A6? In your example, considering five alternatives is a problem. If you add A1 and A2 to the initial, that is other problem. Suppose as a simple example, that you go to a car dealer and find seven models that you can consider, but analyzes only five and obtain a result. Then you add the two other cars and probably will get another selection. What do you gain with that? Probably the two cars will have better and wore qualities that the other 5. You must consider the seven cars at the same time

7- Page 4 “Initially, the ranking was applied to the five alternatives A3, A4, A5, A6, and A7. Therefore, the decision matrix in this case is the same as the one generated when applying the RAM method”

I disagree, why the ranking should be preserved when adding the last two alternatives. You are assuming that there is not rank reversal, without any proof. There could be rank reversal because by adding two alternatives you are adding two new vectors that modify each one of the criteria, and what if one of the added alternatives is better that any of the existent? By the way, in a DOE that I did years ago, varying from 2 to 10 alternatives, totally modify the ranking, and this was proved mathematically. Do you know why?

Because each new alternative I added provided more information on the problem, and already incorporating the former information produced each precedent alternative. Progressively, the components of the old ranking disappeared

These are my comment that I hope can help

Nolberto Munier