I# 119
Dear Tran Van Dua, Duong Van Duc, Nguyen Chi Bao, Do Duc Trung
I read your paper
Integration of objective weighting methods for criteria and MCDM methods: Application in material selection
My comments:
1- Page 2 formula 2
I understand that to compute entropy ej for a criterion the formula is
j= n
ej = It is equal to the sumproduct of a normalized variable and its Neperian logarithm. I couldn't put the formula here.
j=1
2- In page 7 you say “Secondly, the weights of criteria when calculated by the LOPCOW method tend to be opposite to when calculated by the Entropy method”
Entropy is a rational and mathematical method and then, for me, what it shows is true. When using the weights by LOPCOW you get that they are opposite to entropy, makes me think that there is something strange, because both methods are driven by logarithms
Remember that using entropy you get entropy values and the corresponding information values, the latter equal to 1-Entropy. I wonder if it could be that you are comparing the weightsfrom LOPCOW to the information obtained from entropy, which could explain the opposition.
Your Fig 1 appears to confirm this since entropy is always the complement to 1 of the LOPCOW weights. If this is so, then, both methods coincide.
3- Regarding MEREC, I believe that this method, albeit ingenuous, is biased, because in a matrix of say 7 criteria, you are calculating the weight of only 6 each time you change or remove a criterion. Therefore, in all runs you are not solving the same problem, but 7 different ones.
Consequently, in my opinion, you can not include MEREC in this analysis.
4- The very well-known CRITIC uses two metrics, the standard deviation to measure dispersion of values in a criterion, and correlation between criteria, both mathematically correct. That is, measuring dispersion of data in each criterion is the same as what entropy does, however entropy does not take into account correlation, that measures if a pair of criteria is or not monotonic.
That is, through entropy you measure dispersion of values in each criterion individually. Using correlation you measure a totally different aspect, and you have to con sider two variables.
Of course, there must be differences between these two mathematically correct systems
However, if you graphic the values of entropy and CRITIC, observe that both follows exactly the same pattern. Both start with a high value, decrease, goes up again and decrease again. The only difference is given in the magnitude of variation in each case, which indicate different dispersion values as those shown using entropy, and this probable is the reason of the differences.
5- In page 8 table 4, you mention RI scores but do not indicate what RI is
6 – In page 14 you say “Thus, in all three cases studied, it is consistently observed that when the weights of criteria are calculated using the MEREC method, the change in their values across criteria is greater compared to the LOPCOW and Entropy methods”
Your observation appears to confirm what I said in 3), that MEREC should not be compared because it addresses different problems instead of only one, as the other methods
7. In the conclusions you say “If a criterion has a high weight when calculated by the LOPCOW method, then that criterion will have a low weight when calculated by the Entropy me”
As I said before, this conclusion may be incorrect
I hope these few comments may be of help
Nolberto Munier
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