# 141

Dear Luis Serrano-Gomez , Isabel C. Gil-García , M. Socorro García-Cascales, and Ana Fernández-Guillamón

I read your paper article:

Improving the Selection of PV Modules and Batteries for Off-Grid PV Installations Using a Decision Support System

1-In my opinion you should say that you want to compare the rankings when using AHP weights and entropy, for residential PV installations, using different types of cells or modules as you call them. You should also say why batteries are needed, albeit not in all cases, and also that the installation need and inverter to convert cc to ac, unless you use the installation only for equipment such as computers and telephones.

If it is true that there will be two types of results based on two types of weights, however AHP derived weights are good for quantifying or ranking criteria according to their relative importance, while using entropy, you also rank criteria but not for the same purpose, for entropy delivers values regarding levels of information which are based on the contents in each criterion, i.e., the discrimination of its performance values, independently the relative importance of criteria.

What I am trying to say is that entropy deals with performance values that are able to evaluate alternatives y get scores for each one (with mathematical support, which it is the base of Information Theory).

Criteria weights are used to rank criteria and cannot be used to evaluate alternatives and getting their rank. In reality, weights are not such, but trade-offs, useful for compensation and nothing else. In AHP it is assumed, (and thus, with no mathematical support) that trade-offs are equivalent to weights, which clearly is not true.

2- You say “The results show that AHP and Entropy produce contrasting criteria weights, yet TOPSIS converges on similar top ranked alternatives using either set of weights, with the combination of lithium-ion batteries with the copper indium gallium selenide PV module as optimal”

Granted, both, weights from AHP and information from entropy can be used to rank criteria, but on completely different issues. It is like comparing the purpose of a car and that of a truck, both have different functions, different characteristics, demands and use, even when they an share some criteria, like investment, maintenance, return on investment, etc.

You lost me. What is the link between MCDM computation and a physical phenomenon using PV cells and batteries? By the way, optimality does not exist in MCDM. Its purpose is to find the best alternative.

3 -Page 1 “Entropy’s objectivity elevates criteria with limited data variability, potentially misrepresenting their true significance”

What does it mean ‘elevate’? Entropy does not modify data; it simply reflects an existent condition. Data with little variability simply means that it is not very useful for alternatives evaluation.

4- I wonder how it was possible to predict how will be the energy matrix in the 35 years from 2015 to 2050, as shown in Figure 1

What about new developments? For instance, most probably in 2015 nuclear fusion was utopian, however, in this year 2024, only 9 years further, there is a prototype already built in Southern France , called ITER, that started tests. Before you correct me, the nuclear it mentions there is the fission system, exactly the opposite to the fusion system. It does not use uranium but two hydrogen isotopes (deuterium and tritium)

4- In page 3 you pose an interesting series of questions. Please find my comments intercalated (yours in italics)

· How do the criteria weights obtained from the AHP method compare with those obtained from the Entropy method

I already answered this question above. They are not comparable. One are trade-offs, while the other is information, and Shannon’s Theorem proves this.

· Which of the criteria weighting method (AHP or Entropy) provides a more effective foundation for evaluating and ranking PV modules and batteries using the TOPSIS method?

TOPSIS can evaluate, but AHP have nothing to do with it

Obviously, only entropy. The other is simply a wish

• How do the rankings of PV modules and batteries differ when using TOPSIS with criteria weighted by AHP versus those weighted by the Entropy method?

They should coincide if AHP were a scientific tool, but it is not. It is based on several assumptions, intuitions and invented weights

• Can the proposed three-phase DSS framework effectively support decision making for optimising stand-alone PV installations by selecting the most suitable PV module and battery technologies?

Impossible to answer, because optimization is impossible (for instance you cannot maximize benefits and at the same time minimize costs). What all MCDM aim to is to find a convenient and balanced solution

5- In page 4 you say “The three-phase DSS framework developed in this research can be adopted for decision making in sizing and selecting the main components of both off-grid and grid connected PV installations”

Well, now you talk to grid connections? Of course you can make connections to the grid

6- In page 8, in the formulas it is ln not log, and Shannon had a reason fat that

7- In page 13 you detail eight criteria. Did you realize that some of these criteria are interrelated and thus, you cannot use AHP for weighting? Saaty said this, not me, but I agree

8- The criteria pair-wise comparison, is considered and criticized by many researchers, including me, because none of us can establish the value of preference of one criterion over another, because is not rational to expect that somebody can put a value to that advantage. Did you notice that none of the three experts you mention, probably very good in their activates, most probably did not even hear about MCDM? What can they judge?

9- In page 14 “As this method is based on the variability and dispersion of the data for each criterion to determine its degree of uncertainty, the greater the variability in the data for a criterion, the lower its weight, as high variability indicates less useful information”

I am afraid that it is the opposite: The greater the dispersion or variability the larger the amount of information that a criterion contains. Correspondingly, the lower the entropy

10- Page 13 “It should be noted that, with this method, criteria with more consistent and less dispersed data will receive higher weights, reflecting their relative importance in the decision-making process. across the alternatives, the Entropy method assigns the highest weights to those criteria. It should be noted that, with this method, criteria with more consistent and less dispersed data will receive higher weights, reflecting their relative importance in the decision-making”

It will receive higher weights or high entropy, which is useless for decision making.

Remember thast to for a maximum entropy of 1, corresponds the minimum the information, equal to 0

I suggest reviewing this paragraph, because as you can see it is against the theory and common sense.

As un example: You have 3 alternatives and say 5 criteria, and one of the criteria has these performance values: 3 - 3 – 4. As it can be realized the three values are too close, and then their evaluation of the 3 alternatives will be very similar, confusing, or lot of noise in Information Theory parlance, since the three of them evaluate the alternatives with almost the same value. This is high entropy

Therefore, the utility of this criterion is very low. If the values were for instance 4 -8 -10 it is obvious that there is less confusion or less noise, than in the precedent case, thus the entropy is lower than before and the information or (1-entropy), higher, since the scenario is clearer for the analyst

You are confused: In MCDM, high entropy is something undesirable.

What is a binary criterion for you? Normally, it is a criterion which performance values are 1s and 0s

I could continue, but in view of the above I think it is redundant, specially because the faulty interpretation of entropy, and then your conclusions are invalid, in addition of using an incorrect MCDM method.

I hope these comments may help

Nolberto Munier