# 116
Dear Valerio Antonio Pamplona Salomon, and Luiz Flavio Autran Monteiro Gomes
I read your paper
Consistency Improvement 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’
Non really. It is a measure of the coherence of values from the DM using his/her intuition. Now, why this person must be coherent?
For instance, assume that the problem is to address the merits and demerits of a movie, considering criteria such as the plot, the actors’ work, the dialogue, special effects, etc. In comparing the plot and the dialog the DM may say that in his opinion that plot is superior to the dialogue. In comparing dialogue with actors’ work the DM may say, really the dialogue is superior in interest to that of actors; work. Comparing plot with actors’ work he decides that the plot is inferior to a superb work of actors.
Observe that the DM is not contradicting himself, he is only comparing pares of independent criteria
Thus, if
Plot is > Dialogue
Dialogue > Actors’ work
Plot < Actors’ work
There is clear no transitivity, no consistency, and so what? What is wrong with this?
When the DM legitimately gave his/her opinion and feelings, why a formula tells him “You must lower the value of actors’ work and increase the plot value, if not, you cant continue”
Where is the rationality here? Why to force something that may not exist?
The answer is that because there is not consistency, the Eigen Value method can’t be applied, and this is the only mathematical tool that AHP use. Extract your own conclusions.
2. “When an indicator is out of the desired interval, the data must be reviewed”
In other words, a formula is telling the DM what he MUST correct, as if he were a robot.
And if the DM does not agree? A formula is more important that what a human being thinks? Very scientific indeed!
The worst is that with a tolerance of 10%, also estimated, it is assumed that the response must be transitive. Sinc the resulting values are to be applied to real-life scenarios,another assumption without the lightest mathematical and common-sense support, the real problem must also be transitive. This is absurd, especially when in real-life transitivity is not precisely common.
3. In page 3 “One main reason for the AHP’leadership in publications on MCDM is its solid mathematical foundation”
Solid mathematical foundation? So, for you, pair-wise comparison, intuition, assuming that trade-offs are weights, assuming that weights can evaluate alternatives, etc., are solid mathematical foundations? Even the fundamental scale is a false copy of the Weber-Fechter Law of incentives and results.
4. You are right when asserting that AHP is the most popular and used MCDM method. It is true. Do you know the reason?
Because it requires neither analysis, nor research on a certain problem. It is only a matter on using DM’s intuition and mood. In other words, the tool does not require to think, well typical of descriptive methods, against the normative like TOPSIS, PROMETHEE, VIKOR and others.
5. In the conclusions “Consistency measurement and improvement is still an attractive subject of research in the AHP literature”
This is absolutely true. Now my question: What for? It is like writing in water. It is useless
Hope that my comments may help
Nolberto Munier
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