# 152

Dear Valerio Antonio Pamplona Salomon and Luiz Flavio Autran Monteiro Gomes

I read your paper

Iprovemmnet in the Analytic Hierarchy Process

My comments:

1- In the abstract you say “Consistency is a measure of the quality of data input in the AHP “

In my opinion that is not an exact definition, because what it measures is a coherence of the DM estimates. My question, is, when this consistency does not exist, is it reasonable to force it according to what a formula says? Naturally, doing that there would always be a coherence. You call elegantly this action as ‘reviewing’.

And what if the DM refuses to alter his/her estimate, which is the next step? There is none, because the ‘mathematical’ model does not allow to continue. So, the software commands your actions, and dare to correct the estimates of a knowledgeable person.

2- page 1 “One main reason for the AHP’s leadership in publications on MCDM is its solid mathematical foundation”

I disagree, for AHP does not have a mathematical foundation, unless you call that at Pair-wise comparison, making and assigning arbitrary comparisons between two criteria based on intuition, the above mentioned forcing mandatory mechanism to assure transitivity, using a scale or fundamental scale based on a psychological law that says that increasing incentives produce logarithmic responses, and then equalizing arbitrary values to increasing incentives, etc. The only algebraic tool that AHP uses is the Eigen Values of the geometric mean.

3- “Rank preservation or rank reversal”

Since when both concepts are equal, when in reality they are opposite? Rank preservation or ranking invariance appears when there is not rank reversal, and vice versa

4- “Another main reason for the great number of AHP publications is the need to solve practical problems with a handy tool”

I agree that it is a handy tool, but to solve problems, other than elemental situations? Please, just show me a medium complex problem solved by AHP.

This method necessitated to be corrected by Saaty with the ANP, because its absurd lineal hierarchy, is indeed the most used in the world, simple because the practitioner does not need to think, or analyze or research. He just put numbers that come to his mind, press the start button, and voila, the software gives a solution.

5 page 2 “To be consistent means no change of mind. Consistency is “conformity with previous practice”

What practice?

This definition puzzles me. However, do you realize that there is a contradiction? If there is inconsistency the AHP forces the DM to change his mind, like it or not.\

6- Page 11 “After all, consistency checking is an advantage of applying AHP instead of other MCDM methods, which do not include this check. However, when the consistency test fails, the decision process stalls”

And why other methods should be worried with inconsistency if they are not based on the same AHP principle, where consistency appears to be paramount? As a root question, why the estimates of the DM must be consistent or transitive? Is there any axiom or theorem about that? Of course, mathematically if A > B and B >C, A > C, this is an axiom, but why do you think that it also MUST apply to the real world?

As an example, assume a person selecting three different places for a holiday: Stay at home, going to the mountain or going to a beach

Comparing between staying at home and the mountain, the person prefers a mountain and between a mountain and a beach prefers the beach. Does it mean that there is transitivity here because Home > Mountain > Beach?

Perhaps not, because the person may not like very much staying at home. This is real life. What AHP does is transfer the DM preferences arranged consistently to and environment that may be not transitive. I asked this question many times and still waiting from and answer.

Why there is not answer? Because it is an irreal scenario. So, why so much importance to consistency or inconsistency? What for? To justify a method that is already flawed?

These are some of my comments

I hope they can help you

Nolberto Munier