# 166

Dear Imad Hassan, Ibrahim Alhamrouni and Nurul Hanis Azhan

I read your paper:

A CRITIC–TOPSIS Multi-Criteria Decision-Making Approach for Optimum Site Selection for Solar PV Farm

My comments:

1- In page 9 you say “PV systems work most effectively in vast land areas with abundant solar irradiation throughout the year. However, there is a number of major obstacles impeding the development of PV technology, one of which is the difference in solar irradiation brought on by various geographical factors in various places”

I do not think that it is an obstacle, as you say about the different irradiations, simply they will produce different amount of electricity in different places. Where is the obstacle?

2- Page 3 “In most of the previously published literature, the AHP technique, which is based on subjective values, is typically used to give weights to the criteria. However, the CRITIC method, which is based on objective values, is now being used in this work for the first time to do so for PV system site selection”

I am not sure that this assertion is realistic, because I have seen some, although not many works, using CRITIC or Entropy

3- Page 3 “The advantage of the CRITIC technique is that it helps to provide an objective and unbiased approach, ensuring that the selected sites are technically feasible, socially and environmentally responsible, and economically viable”

I am afraid that I do not concur in all your sentence. It is true that the CRITIC method provides an unbiased approach, but it cannot prove that the selected sites are technically feasible. It depends on multiple interrelations between criteria and alternatives, something that no MCDM method consider except Linear Programming (LP). Actual methods only add individual contributions, while LP considers intersections between them.

Thus, comparing criteria C1 and c2 and adding them up, actual methods simply express a sum, or that

C1 ∪ C2 , or ‘Union", while C1 ∩ C2 indicates multiplication or “Intersection”. With union you cannot indicate the influence of C1 on C2 or vice versa, but you can, by using Intersection, indicating multiple relationships and sustainability, as shown in the Venn diagrams, expressing that the three legs of sustainability, Economics, Social and Environment, must intersect. That is easily done by LP and indicates that all legs are considered simultaneously.

4- Page 3 “The CRITIC method determines the relative importance of criteria by analyzing their intercorrelations and impact on the overall decision without relying on subjective judgments”

In my opinion, it has two different actions. One analyzes the discrimination between performance values within each criterion, by using the standard deviation. The other, analyzes the relationship of criteria among themselves regarding the relationship of each pair through correlation, that is, if both are, or not, increasing or decreasing at the same time, that is, the behaviour of one criterion is similar to another. As far as I know, the discrimination is affected by multiplication with the sum of (1- correlation coefficient), this one representing the conflicts between criteria.

In my opinion, this second step in unnecessary, since I do not see why discrimination should be affected by criteria correlation denoting conflicts among them

The paper speaks about feasibility, but what is it? In my opinion, if you have, say 9 criteria or objectives, like speed, comfort, cost, style, etc., feasibility means that there is a solution when all criteria are taken into account in a greater or lesser degree. Google defines it as follows:

“Feasibility involves assessing whether a proposed solution is viable, practical, and achievable within the given constraints”

For instance, if purchasing a car, selecting among different makers, subject to a set of criteria like maximum speed, comfort, cost, style, etc., the purchaser selects one (a solution), but due to that it carries a price tag that he cannot afford, the solution is not viable, because it is not achievable as per cost criterion, since it falls short of that price. Therefore, as normally everybody does, you must have a target for each criterion or objective, it does not matter its nature. It can be dollar value, size of manpower, CO2 maximum discharge, speed, etc.

5- Page 12. It looks wise and reasonable to proceed with a prior selection of cities that receive a minimum irradiation value of 5KWh /m2 day, however, it implies that you have selected arbitrarily an objective as the most important (irradiation), and it could be that it is not so, because those places, albeit good for generation considered individually, could also be affected by other factors that decrease that advantage. In my opinion, all 15 adequate cities in the country should be considered, with their known irradiation values, as in the other criteria. Leave for the software the task to make the arithmetic comparisons.

This is contrary an what you say “By selecting these particular cities, the study can offer a more thorough analysis of the potential benefits as well as challenges of putting solar PV power projects into practice in Saudi Arabia”, and it is unfair, because other locations, ALL criteria considered SIMULTANEOUSLY may offer better locations

6- Page 14, you give formula 6 for information measure of a criterion; that is incorrect. That information is given by the Shannon formula of entropy. As per my understanding formula 6 measures the lack of a perfect correlation between criteria, multiplied by the standard deviation. As that, it only indicates that dispersion or discrimination in a criterion is less than that computed by standard deviation, in other words it demonstrates that data is more concentrated, but it does not give a value of the information.

The information (I) = (1- entropy) of each criterion, and the entropy is given b y the Shannon’s formula; I remind you that this is backed up by a theorem.

7- Page 16 “The correlation matrix is calculated by comparing the performance of each criterion with every other criterion, and the information measure (H) represents the degree of redundancy or overlap between the criterion and all the other criteria. The higher the information measure, the less redundant the criterion is with respect to the other criteria and, therefore, the more important it is in the decision-making process”

I find this paragraph very interesting. In reality, ‘H’, as the product of standard deviation ‘σ’ and the summation of the complements to 1 of correlation ‘ρ’, modifies ‘σ’, deceasing it for large correlation and increasing for weak ones, but I believe that there is no redundancy or overlapping between two criteria, it is simply that the ups and downs of their performance values follow the same pattern. In addition, there could be overlapping when the two criteria refer to the same issue, for instance cost, but how can be overlapping between criteria environment and school enrollment?

Why do you assume that this operation defines ‘information’? Information is a realm of entropy, and I do not see any relationship of this formula it, especially taking into account that information, as per Shannon entropy is an exponential function.

8- Pag 18 “This study illustrates how energy planners and policy-makers can implement and evaluate a strategic decision-making process by combining CRITIC and TOPSIS approaches”

Neither TOPSIS nor any other MCDM method, except Linear Programming, process the initial matrix as a system, i.e., is holistically; they use addition in lieu of multiplication, and as a consequence, getting a result that is the sum of parts, when it should be the intersection of parts, like for instance, when defining sustainability. In here the Venn diagram defines a place where reside the different intersections between Economics, Social and Environment

9- On page 8 you use an old cliché very common in MCDM, very often cited, trying to validate a result by solving the same problem by different methods, and comparing results. Unfortunatelly, that procedure is useless, because it does not have any mathematical support, it is only an assumption based on intuition. Validation is impossible in MCDM for any method, because there is not a yardstick that can used to compare result to.

10- Page 20, you speak about sensitivity analysis, which certainly is able to validate the strength of a solution. But for that, you need to know which are the criteria that are responsible of that solution. You do not have that information, and normally intuitively it is selected the criterion with the largest weight. This does not have any mathematical support, let alone, to select one criterion and keep all the other constant (the ceteris paribus economics concept). If you compute the objective weights from entropy, most probably the criteria importance values will be different.

By the way, weights have no role here, what is really significant is the importance of each criterion based on their resources. If you increase resources progressively, the criteria effectively participate lineally, and will also indicate how much you can increase/decrease each one, without perturbing the best selection.

This can also be easily proved in your own computer.

These are my comments, hope they can help you

Nolberto Munier