Dear Nguyen Hong Son, Tran Trung Hieu, Nguyen Manh Thang, Huynh Nhu Tan, Nguyen Tien Can, Nguyen Chi Bao

I have read your paper

CHOOSING THE BEST MACHINE TOOL IN MECHANICAL MANUFACTURING

And these are my comments

1- In the abstract you say “A machine is considered to be the best only when it is chosen based on all of its criteria”

This assertion is confusing because it appears to mean that a project is selected by ALL criteria, when normally, only some of them participate. Which is true, is that the alternatives must be SUBJECT to all criteria, but the selection is made by the MCDM method that indicates the best machine.

You don’t need two methods for this, using the appropriate method is enough.

2- You declare the purpose of this study as “The objective of this study is to determine the best solution in each type of machine”

Well, this is in general the objective of most MCDM models for most types of alternatives, i.e., a selection of something. The fact that you work with three different types of machines, only means that you are working with three cases or problems.

3- You say “The selection of these two distinct methods is intended to produce the most generalizable conclusion”

Sorry, but than sentence is very vague. What is a general conclusion?

The number of methods you use probably will give similar or different rankings, and even in the first case, it does not guaranty that the ranking is the best.

4- “On the other hand, in published studies, there is only one certain machine type that is chosen in each study. In order to add more useful information to this research direction, in this study, three different types of machines will be selected simultaneously, including grinding machine, drilling machine and milling machine. This is the reason why this study is performed”

Selected simultaneously? Let me see if I understand the problem

You have three different types of machines, for grinding, drilling and milling.

For the first you have 12 criteria, 13 for the second and 9 for the third.

In each case you apply two MCDM methods to decide which is the best in each type of machine.

This is correct and normal. In reality, the article addresses three different problems, and using the same FUCA and CURLI methods in the three of them. Different would be the case if you mix them in on decision matrix and with three sets of criteria. And ask, for instance, to minimize cost.

5-What I don’t understand is which is the purpose of this exercise.

You demonstrated that with FUCA and CURLI methods you reach practically the same rankings.

I was looking the rankings in each case and was surprised by the coincidences, especially considering that you are working with 12 and 13 and 9 alternatives. This coincidence denotes a high degree of correlation between both methods, and that is what called my attention, because it is not normal.

I was thinking about the reason of this very close correlation, and arrived to the conclusion that it may be due to the fact that both algorithms follow the same procedure, that is, for each criterion and using FUCA, selecting the largest value and thus, permitting the alternatives ranking, and in the case of CURLI, the process is practically the same because it finds for each alternative differences for each criterion, and indicates it with 1 and -1.

In my opinion, the article in itself with your objective, is not a novelty.

However, what is new is the coincidence between FUCA and CURLI. If it is true that this proves nothing regarding the best solution, because we don’t know which is the real ranking, it proves a very important point, that I have been talking during years. In your example you don’t use any type of subjectivity, and it supports my hypotheses that the fact that different methods, addressing the same issue and aiming at the same goal, should give the same results:

Your example supports this; you get the same results, using two different methods because there is no subjectivity. Probably, if you apply weights in FUCA, the result will be different.

I hope this help

Nolberto Munier