# 129

Dear Sarra Daimi, Sonia Rebai

Sustainability performance assessment of Tunisian public transport companies: AHP and ANP approaches

My comments:

1. In page 4 you say “Although each method has its own techniques and measurement tools, they all share the same purpose and follow similar approaches”

Not really, all methods look for finding the most convenient or compromise solution, but normally, the approaches are dissimilar. AHP is different to PROMETHEE, which is turn, is different to ELECTRE, to VIKOR, and so on. Some methods like AHP are descriptive and most of the others are normative.

2. Pag 4 “AHP, introduced by Thomas L. Saaty in the 1970s as a MCDM approach, has grabbed the attention of an enormous number of researchers due to its simple mathematical properties and its high-level accuracy”

No doubt that AHP has grabbed the attention on an enormous number of researchers, too bad that you do not mention that an also enormous number is in disagreement with different aspects of the method, for both AHP and ANP

Mathematical properties? Which, other than using the Eigen Value or the geometric mean?

It incorporated however, many assumptions and beliefs that Saaty never explained.

High level of accuracy? How can it be demonstrated if non MCDM can claim that, because there is not a yardstick to compare to?

Accuracy? Working with invented weights derived from the DM mood or intuition?

AHP is not able to solve complex problems, because they do not follow the lineal top to down hierarchy. The method was not created for that.

3. Page 4 “This paper adopts AHP direct rating approach, which sets-up intensity scales for each criterion; contrarily to AHP relative approach, which uses only the pairwise comparison as an assessment tool”

This is a very good approach; it makes a lot more sense rating a criterion by itself than the non-sense pair-wise comparison

Page 4 “Thomas L. Saaty [55] also developed ANP as a generalization of AHP to process the several applications that cannot be converted into a hierarchical structure due to the criteria interactivity”

This is absolutely right; however, I am puzzled. How can you compare the results from solving a problem with AHP with the solution for the same problem solved in ANP?

If there is dependency among criteria, and there is a lot in your example, how can you solve it by AHP?

Naturally, modelling a problem in AHP and then in a lineal hierarchical structure, and also solving it in ANP, is feasible, since there could be lineal hierarchies in a network. But what do you intend to prove?

4. Page 5, Figure 2, in there you established that ANP ‘Connect interdependent criteria’, therefore, you admit that in your problem criteria are not independent, if so, you can’t use AHP, but you do

Page 5 “Transitivity axiom implies that when preferring A over B and B over C, A must definitely be more preferred than C”

Yes, in mathematics, not always in real-life. Who can guarantee that what results that appear in your computer screen using AHP, is applicable to the real-world? You know the answer: Nothing

It is only a free and very convenient assumption, which, in addition, may change with another DM, and thus meaning that there are two realities. Have you seriously thought about it?

“CR thus reduces the level of errors and bias by allowing the practitioners to detect any unintentional misjudgment in comparisons”

Apparently, you forget that it is a formula that corrects DM, and obliges him to comply, in order to guaranty transitivity? Now I ask: Why there should be transitivity in the DM judgements?

“After criteria prioritization, alternatives are directly rated, one at a time”

Yes, but altered because they are multiplied by a common criterion weight that affects to all of them. It is very easy to demonstrate that criteria normally are not constant because they depend on the alternative under analysis. So, criteria invariance is another wrong assumption

5. Page 6 Fig 5. This hierarchy is not lineal since ‘Average fleet age’ for instance is linked to safety, cost efficiency ratio and many others. Surely the experts know this, but they probably ignored that AHP demands criteria independency

6. In page 8 “One can conclude that companies’ behaviours vary as the priorities of the main criteria change”

And how do you know which is the main criterion? Just because it has the largest weight?

If this is so, this is another false assumption, because, even if this may be intuitive, it can be proved that it is not always certain. It could, as well as it couldn’t be the main criterion, since their relative importance does not depend of a subjective weight but in the capacity for evaluation the alternatives, i.e. it depends from the entropy of each criterion

7- In page 8 “to reveal the degree of correlation between the two sets of rankings resulted by AHP and ANP methods”

Of course, since you are forcing the issue when using AHP and ANP, both with the same problem.

8- In page 8 “These findings indicate at least the robust[1]ness of the ranking of the top three companies”

Where did you get that conclusion? Robustness has nothing to do with this.

9- In page 8 “AHP performance sensitivity is conducted on 5 different scenarios. In each scenario, the priority of one of the dimensions is changed, as shown in Table 8”

This is not realistic, because you have to consider all ‘scenarios’ as you call the changing of criteria, AT THE SAME TIME, not separately. This is another AHP invention that does not have any mathematical support. If you do not believe me, ask an economist

There are more issues that in my humble opinion are mistaken, so I prefer to stop here.

I hope that my comments can help you

Nolberto Munier