# 105

Dear Yingfang Li , Xingxing He, Luis Martínez , Jiafeng Zhang , Danchen Wang , Xueqin Amy Liu

I read your paper “Comparative analysis of three categories of multi-criteria decision-making methods”

My comments

1) In the abstract you say: “However, in spite of the multiple methods, it is common that different of them provide the same solutions”

It is exactly the opposite; it is most common that different methods normally produce different solutions. There is a myriad of papers about this

2) In page 1 “If different MCDM methods achieve contradictory solutions, then the correctness of the choice of each of them is questioned.”

You contradict yourselve with what you say in the abstract.

3) “selecting the most appropriate MCDM method can be considered as an MCDM problem””

Agreed

4) “Few literatures compare various MCDM methods theoretically, for example, through their normalization methods and calculation process”

Agreed

5) In page 2 “However, few efforts have been made to investigate why different MCDM methods can achieve the same solutions or why the same solutions can be obtained by using different normalization methods in a MCDM method”

If all methods start from the same decision matrix, aim at the same objective and use mathematical relationships, all methods should yield de same result. They don’t, because the respective algorithms are affected by different kinds of subjectivity, like using invented weights for criteria, as well as different assumptions, which are no more than suppositions

Your second paragraph is a completely different problem, and it is unavoidable, because most MCDM methods are based on comparing distances between alternatives and different normalization methods produce different distances.

6) “providing some modified MCDM methods”

This method was created in the 50s and it is Linear Programming, where alternatives do not depend on distances, and then, the different normalization procedures give the same solution, and of course, this can be proved.

7) “However, few extended forms of various MCDM methods considering general normalization methods and distance measures have been proposed in the literature”

And how many of them worked?

8) ” Criteria (known as attributes or decision factors)”

Criteria and attributes are not equivalents. Attributes are the characteristics of the values in each criterion

9) “In this paper, we have made a provision to delete such criteria before making decisions such that all of the selected criteria are meaningful”

Incorrect approach from my point of view, because even if it is zero the information a criterion with identical values for all alternative provides, it still influences the other criteria and may be able to modify a result, since it can modify the polygon or closed convex space where all feasible solutions lie. This is easy to demonstrate.

10) “The normalization of criteria is indispensable in order to eliminate the variances among different criteria”

Not really, the purpose of normalization is to reduce all criteria values to a common unit.

11) “The first gap is related to estimating the causes of the same solutions in MCDM methods”

And which is that cause? In my opinion it is like asking which are the cause by which 2 x 3 = 6

12) Page 20 “examined the causes of the same solutions from different MCDM methods”

And which are they?

13) “why different normalization methods can achieve the same solutions in a MCDM method through the theory of MCDM methods”.

And where is that explanation?

14) “We also studied the relationship between different MCDM methods and discussed the characteristics of various MCDM methods by category and compared their evaluation indexes”

Ans what is the result of that study?

15) “Therefore, we consider comparing the extended MCDM methods with traditional MCDM methods in the future work, and examining the impact of different normalization methods, measurements, aggregation functions on them”

What for? What is it to be gained?

16) “. Mohtashami (2021) developed the best-worst method for considering fuzzy pairwise comparisons (FBWM) by proposing a new fuzzy mathematical model which yields crisp weights from a fuzzy pairwise comparison matrix’

Don’t you think strange and devoid of all logic, the fact that you apply a proven and scientific methodology like fuzzy, to invented values?

What is the purpose of apply fuzzy to a value that has been obtained by intuition, and by making a very arguable comparison, without any mathematical foundation, using pair-wise comparison, another no mathematics procedure?

17) On page 21 “In order to obtain more accurate decision results, it is necessary to conduct sensitivity analysis from both criteria values and criteria weights simultaneously. In the future work, we will also consider a sensitivity analysis that combines criteria values and criteria weights.”

Sensitivity analysis is not meant to produce more accurate results, but determine the strength of the best solution, and not precisely using subjective weights

I hope it helps

Nolberto Munier