# 194

Dear Jakub Więckowski, Paweł Białoń, Wojciech Sałabun

I read your paper:

Comparative sensitivity analysis of single and multiple modifications in multi-criteria decision analysis

My comments:

1- In page 3 you say: “However, existing studies primarily focus on different criteria-weight scenarios, leaving an unexplored gap in the simultaneous modification of multiple values within the decision matrix. This paper integrates sensitivity analysis within the MCDA methods, extending its role in the comprehensive assessment of decision problems.

Reference is made to the underlined paragraph. You are right on what you say, especially considering the simultaneous modification of multiple values, which is indeed a little explored area, if any

2- You also say “Sensitivity analysis becomes crucial in offering decision-makers a broader perspective, aiding them in navigating the complexities of decision-making in dynamic environments”.

However, in my opinion, your get short in assessing the importance of sensitivity analysis (SA), since it is a mandatory procedure, albeit you focus on matrix values, instead of the values of criteria, which is the more common.

As a proof of concept your idea is feasible, but I think it is not realistic, and I will explain this assertion

As I understand, the paper refers to one of the forms of SA, i.e., to investigate the strength of the best solution when performance values in the decision matrix are changed either by increasing or decreasing, different to the other SA that analyzes the strength of the best solution when you change the value of whole criteria. However, both have the same type of effect, that is, possibility to alter the ranking of alternatives, and both work with the same values, the first with those within a criterion, and the second with the total value of the criterion.

3- “problem evaluations were developed, considering different approaches for examining the robustness of the results [31]. Those frameworks proposed a methodology for evaluating Management Option Rank Equivalence (MORE) approach [21, 20], identifying the most critical criterion [28], examining the ranking robustness to the Rank Reversal (RR) paradox”

I do not know what frameworks you are referring to, but I am sure that RR is not linked to them, for frameworks have no links with robustness. The latter is related to the best alternative keeping its position in a ranking, when a criterion is increased of decreased, and depending on its allowable variation, that certainly may produce displacement of an established ranking.

RR is a geometric natural condition, and clearly not a paradox, related to adding or deleting alternatives, something not linked to SA.

4- “A more beneficial approach could be utilized by examining simultaneous changes in multiple values, which reflects the intricacies of real-world decision problems more accurately’

Exactly, but unfortunately, ignored by 99% of the SA procedures, that consider that OAT or ceteris paribus, is correct, without any mathematical support

5- “A more beneficial approach could be utilized by examining simultaneouschanges in multiple values, which reflects the intricacies of real-world decision problems more accurately”

Very true, and also not considered by most SA methods

6- “Moreover, existing approaches in this direction remain underdeveloped, limiting the extraction of potential insights from sensitivity analysis in the results from the MCDA methods. This highlights an apparent research gap that should be thoroughly investigated”

I am afraid that you are not aware that this has been investigated, and simultaneous changes in multiple values can be done easily using the SIMUS method (Munier, 2011)

7- At the beginning I said that your method, even considering that is a great advance over the conventional MCDM more that 200 methods, is not realistic, and I detail here are my reasons after examining your example.

a) It does not identify which are the criteria that are significant for the alternative selected. As I understand, you consider them all. In your example, C2 is irrelevant, according to your problem that I solved by Linear Programming (LP) that gives mathematically exact results, not approximations. Therefore, considering variations in C 2 does not modify the ranking, and this can even be visualized in a simple graph depicting the two alternatives as throe axes of a coordinates system, and the criteria by straight lines.

b) Your increasing is arbitrary, and most important, it does not take into account if they are allowable variation or gap for each criterion or in the performance values. It could be that one of them, say C3, cannot be increased in 0.3.

It does not consider that SA must be done for each alternative, and that the selected alternative may be affected by different criteria

Your example: “For three criteria in the problem, bounds B could be defined as B = [3, 2, 4], meaning that the value of the first criterion would be modeled in the range of 3% modification (b1 = 3%), the second criterion in range of 2% modification (b2 = 2%), and third criterion in the range of 4% modification (b3 = 4%)”

And where these values come from? I do not think that this realistic. They are only assumed values

c) You are using several MCDM methods, and all of them do not represent reality, because each criterion is considered independently, when they should relate as a whole and simultaneously

The result from LP indicates that A1 and A2 have the same score, and then, have the same importance, and that C3 is the most important criterion, with a value or weight of 1.79, while C2 = 0

Solved by SIMUS, which is heuristic, and cannot give optimal solutions like LP,gives the same scores for A1 and A 23 than PL

It also shows that C2 =0, same as LP, and that C1 and C3 may have an infinite increment and a decrement of only 0.5

I would be glad to share with you colleagues, my calculations.

These are my comments, hope they can help

Nolberto Munier