# 200

Dear Lázaro V. Cremades, Antonin Ponsich

I read your paper:

Simple and objective determination of criteria weights for evaluating alternatives when using the Analytic Hierarchy Process

My comments:

1- In the abstract you say “In both design and project management, it is usually necessary to make decisions based on criteria that, in many cases, are not completely objective”

True, and for the same reason, there is no need to add more uncertainty using pair-wise comparisons

“The construction of the pairwise comparison matrix is the most critical element of the AHP method”

The AHP has more critical aspects, but arbitrarily establishing by intuition a ratio between two criteria is irrational

“The applicability of both options is evaluated using hypothetical cases compared to the rank-order centroid weight method, and an example taken from the literature.”

As I understand it, option A is the method used at present, while option B consists in finding the average of weights and them measuring distances and ranking according the magnitude of the distances.

For me, this second option is more reasonable, but a question arises: Where the original weights come from? Do you rank criteria individually in a certain scale, fin ds its average, and then compute the distantness between them? If it is so, this appears to be reasonable.

2- In page 1 “Subjectivity in decision making may appear, especially at three moments in the process: a) when choosing the criteria to be used for decision making”

Not in my experience, if the DM consults the different stakeholders related to a project, they can tell him what he needs to consider in each area, and it does not matter if they are in agreement or not between them; the DM would be only independently asking to each stakeholder what must be considered in his/her field. However, in this second case, you cannot use AHP, because there will be performance values for each alternative and each criterion, something that you do noy have in AHP, which incidentally, is the way used by all MCDM methods, which is by far more rational with objective criteria, and for subjective criteria when the DM follows procedures as consultation, polls, surveys, etc.

3- It is refreshing that the authors, showing impartiality, enumerate nine weakness of AHP (there are many more). Unfortunately, they do not say what are the positive aspects of this method, that in my opinion is telling a user that industrial, commercial or technical problems can be solved just by filling a matrix with subjective values, without too much thinking, with no reasoning and no research, even when they come from several DMs, who may reason, investigate, and consult, but in many cases comparting criteria which content they do not know about, let alone agreed, as you correctly point out in other paragraph.

Always in my opinion, AHP, as most MCDM methods, are based on adopting convenient mathematical assunptions, and blatantly ignoring reality, the most common, is to add-up results obtained for each criterion, when, in fact, all criteria should be considered simultaneously, that is, nou using addition but intersection. The only MCDM method that does this is Linear Programming using the Simplex algorithm which by the way, is in all computers of the world, in Microsoft, using Excel and the macro ‘Solver’ that is in ‘Data’, albeit it has the drawback of working with only one objective function. This is circumvented by using the SIMUS method

Real-world problems do not contemplate individual criteria but how each one affects and complements others. Consider for instance a construction project that depends on many criteria like manpower, funding, weather, geological conditions, etc. Fort instance you can not perform earthmoving, which is one criterion, if you not consider at the same time the necessary capital to buy equipment, which in turn depends on invested capital, which may be related with bank loans, etc.

AHP can perhaps be valuable in personal and trivial scenarios, like selecting a site for a holyday or a restaurant to dine. Why?

Because the consequences in these cases, good or bad, fall on the interested person that made the decision, and that affects his/her interests, which does not happen when a project involves thousands of people that did not participle in the project, and have not even consulted. I suggest to read the Arrow’s Impossibility theorem about this.

4- Page 4 “Sort the n criteria in order of importance”

How do you determine for instance in a construction problem that criterion “number or workers” is more or less important than criterion “experience”? Both are mutually important, since if the construction crew has little experience, they cannot perform the job properly, or if hey are very experienced but short in number, the job also is affected. And of course in some subjectivity comparisons between for instance love and tenderness, that comparison is impossible.

5- Page “To check the matrix M for consistency”

In AHP, if consistency does not exist, don’t worry, it is forced to be, in other words, there is a formula that decides, instead of a human being. And most important, what is the consistency of a team of experts important, if the reality may not be consistent? Therefore, what this consistency is good for?

AHP imposes the real-world to adjust what humans want. Saaty himself recognized that this procedure is not always correct.

6- Page 6, Table 1

Am I correct in assuming that you consider that in all 13 different cases the rankings of criteria are always the same as the former but adding a new criterion? Even for hypothetical cases this is very strange

7- In page 16 “The main difference between the proposal introduced in the present work and the AHP method lies in criteria comparison, performed through an ordering of criteria here, while a set of pairwise comparisons is to be carried out in the canonical technique”.

In my opinion, using the canonical technique of partitioning data in two sets and finding if they are related is incorrect in MCDM, because ALL criteria must be compared simultaneously. Most possibly the three restaurants meet your preferences, but there is one that satisfies them better, and this is what you are looking for.

Please consider this trivial example as an illustration:

Suppose that you must select among three alternative restaurants to dine, all of them subject to the same set of criteria [Price, (min), quality of food (max), pleasant atmosphere(max), noise (min), service (max), etc.]

Of course, each restaurant may in some criteria be superior or inferior to other. You need to find a restaurant that satisfies most of your preferences; this is the MCDM problem objective

Probably the three restaurants are feasible solutions, but only one of them will incorporate most of the demands that you have in the set of criteria. Therefore, you cannot analyze the three criteria independently but all of them at the same time.

8- Page 16 “Although this pairwise comparison working mode was justified by Saaty (2008) by the fact that comparing two features is easier than proposing an ordering of many of them. However, the quantification of the priority of a criterion over another one is not only difficult to achieve, but may also lead to undesired rankings”

I agree with Saaty and with you, and as a fact, we humans do that many times a day, it is valid to say that ‘I prefer this criterion over this one’, but being forced to establish a ratio is absurd. If a DM is hiring people, do you think that it is rational for him to say for instance, that background of a applicant is 4 times more important that expertise? Not in my opinion, and AHP says nothing about it.

And what is worse, it applies the same rate to all candidates, since that number does not change irrelevant the candidate, as if background and expertise were identical for all candidates.

This reveals that AHP does not work with the real world,but with abstract assumptions

9- “…, In addition, a DM may not have expertise in all these areas and, therefore, might not be able to appropriately rate his/her preferences, or only intuitively rate them (which may have significant consequences on the final criteria weigh” “[the] DM should be a multiple technical expert” to be able to comprehensively compare criteria numerically.”

Very good point!

I have been saying the same thing during years, but as far as I remember, you are the first or the second to also mention it. Apparently many AHP users do not even notice this evident non-sense of quantifyingpair-wise comparisons.

10- “When asked to evaluate their priorities, populations that are not used to electricity services were barely able to understand the abstract concepts of energy and power, and it was even more difficult for them to compare and, in addition, evaluate numerically the magnitude of their”

Another excellent point! It is good that people must be consulted, but it is unreasonable to ask people make a judgement which is also difficult to experts. But again, AHP defenders also keep mute about this.

11- “Therefore, C1 is implicitly four times more important than C3, whereas the DM still has a slight preference regarding C1 over C3. It is clear that this would not happen when using the simple ordering proposed in our work”

Very good example of the irrationality of assuming that the matrix must be transitive. Which is the reason for that and why AHP put lot of emphasis on it? Why it is not explained? Simply, because the DM can be not coherent hid/her estimates because is a human being, not an algebraic formula

12- “Finally, considering the inherent issues mentioned for the AHP (for complex problems)

Since complex scenarios require a lot of criteria that are interconnected vertically and transversely, AHP, that works only with top-down vertical relationships, cannot be used. We cannot blame AHP for this, simply because it was not created to deal with complex scenarios. It is the people, that was made to believe that filling a matrix with the values a DM has in mind, the DM can be solved.

These are my comments hoping that they help you

Nolberto Munier