# 189

Dear Mališa Žižović, Miloljub Albijanić

I read your paper

An Implementation of the Entropy Method for Determining Weighing Coefficients in a Multicriteria Optimization of Public Procurements

My comments:

1- In the abstract you say “Determining the weights of criteria is a key problem in multicriteria analysis models”

Not in all MCDM methods. Some do not use them. They generate them based on inputted data and other factors. No human participation

2- “The results show that the Entropy method shouldn't be used as a correction method because in most cases, the decision maker Also shows that applying the Entropy method in MCDM problems for determining weighing coefficients can be counterproductive”

We need to understand what a correction means. By the way, I do not believe that you can compare entropy values, with a strong mathematical foundation with subjective weights that are inventions of the mind, and also two different entities with different purposes

3- “These coefficients have to be defined in advance, or a method for determining them has to be given.”

I disagree, because the DM cannot know the result of all interactions for each criterion

4-“We assume that all criteria are of maximizing type, which means there is a preset rule for transforming minimizing type criteria into maximizing type criteria(it is obvious that minimizing type criteria exist, at least one, such as the price of the public procurement)

This is an elemental definition that does not tell the truth, because maximization also means the maximum value equal or less than a limit, (you cannot use more money than you have) and the opposite for cost, which is the minimum value above a minimum limit (you cannot reduce your cost to less than the production cost)

5-“Then, using the algorithm, we calculate the entropies simply by adding all the values in each column from the previous matrix, and then the results are divided with the largest possible value for the Entropy. Then, we subtract these values from number one and get deviations, which can be seen in Table 4a.”

In reality, entropy works with the sum of values, not with the greatest one, and there is a reason for that.

6- Page 5, Table 3. I was working to understand how you obtain the values in this Table. For instance, considering a11 = 0.21 in Table 2, its entropy is 0.21x ln (0.21) = - 0.327, and you obtain value of 0.4728. positive, when it should be negative, since ln(0.21) = -1.56.

In my opinion, the reason ifor this discrepancy is that you multiplied – 0.327 by K =ln (4) = -1.386, and got 0.4533.

There are two errors here:

First, you must multiply by -K = 1/ln (5)= -0.6221, because K is used to find an average of the FIVE alternatives, not for the FOUR criteria

Second, you cannot multiply each aijby K, but by the sum of the FOUR individual entropies, in a criterion

In addition, to normalize you must divide by the sum of FOUR entropy values, not by the greatest value. as you did, you got C4= 1 and then, it means that d = 1 – 1 = 0, that is, zero information, when in reality this value is 0.70 and defining C4 as the most important criterion

I performed the calculation and the entropies are:

C1 =0.03, C2 = 0.10, C3= 0.18 and C 4 = 0.70

7- I have never seen that the weights are given to the bidders. For them it means nothing, since this si a MCDM problem of which most probably they do not have he faintest idea

8- Page 6 “. From here, we naturally have a question: Is 14 f such an important value for the choice and for making a decision that it justifies an increase 4 w to this level? This question has no answer, especially because the value in dispute is the lowest value by the criteria 4

I can give you the answer. They do not have the least importance because weights do not participate in the evaluation, unless they are from entropy. Of course, this can be demonstrated

9- Page 7 “Our question is: can the newly introduced alternative in the Entropy method give completely different weighing coefficients compared to the one from the previous example? If the differences are not small, our decision-maker should at least be aware of that possibility”

Yes, because in adding a new alternative we are also adding a new vector which values have to be considered in calculating the new entropy for each criterion. We have a new sum for each criterion, and that can alter the discrimination of values within it, and in so doing , its entropy may change

10- Page 7 “ If the new alternative with the highest value for the first criteria is added to the starting decision making matrix, the values are below average in the other places”

I do not understand why you are considering on ly the first criterion. If you add an alternative most probably it will have different values for all criteria. Why only for the first one? Why are you assuming that it can affect only one criterion? It is difficult for me to understand your reasoning on the subsequent paragraphs. For the same reason I do not understand about your ‘variants’

11- Page 11 “We can conclude that "the fictitious bid has done a good job when we have weighed coefficients in advance." Whether the first bidder can "secure the job" can be even more radicalized so that the first bidder can introduce two, three, four, or five similar fictitious bids. What will happen in these situations?”

In my opinion you are creating a situation of adding fictitious bids after receiving the offers. I never have seen something like that, and mainly, with what purpose? This is not a Montecarlo simulation exercise but real life.

Sorry, but for me this is irreal. It is only a matrix exercise.

12- Page 16 “In short, the Entropy method is not a method to be used in this area of multicriteria optimization and for determining weighing coefficients at public procurements”

Naturally, what entropy does is identifying the criteria that are really significance for alternatives evaluation, but it does not select them

Entropy per se, cannot select the best alternative; it only gives more importance to the characteristics of each criterion to evaluate alternatives. If most value within a criterion are very close, the criterion is not useful for evaluation because all alternatives will be affected by similar values

As a typical example, if you cast a dice, there six equal probabilities of appearance. The entropy is 1 because the uncertainty is maximal and you do not get any information. If the dice is altered, this identity of probabilities no longer exist, and the thrower gets some useful information, because certain number have higher probability of appearance than others. The same in MCDM

These are my comments. I hope they can help yon

Nolberto Munier