# 191

Dear Jonathan Barzilai

I read your article:

Notes on the Analytic Hierarchy Process

My comments:

1- Abstract: “This progress report outlines the main reasons why Saaty’s Analytic Hierarchy Process (AHP, see [17] and [18]) is not a valid methodology.

I would say that I agree since it has not been designed to address not even medium complex projects, however, it can be used to solve personal and trivial problems where intuition and personal involvement are important

2- Page 2 “Unfortunately, as we will see below, other aspects of the MHP are the basis of common decision methodologies errors.

Absolutely true. The MHP/AHP following a lineal hierarchy, inherited from the army, only considers one direction ‘top-down’ with no room to transversal relationships which are common in all projects.

3- Page 2 “In addition, the use of the eigenvector method to implement the procedure where is the preference reconciling inconsistent input is a mathematical error. As a result of this error, the output of this procedure depends on the description of the problem — an unacceptable property of any algorithm”

I do not know if it is a mathematical error, but I am convinced that forcing a matrix to be consistent is an aberration, just to justify the use of the Eigen Value method

4- Page 3 “As we will see below, the procedures provided by the MHP/AHP for computing the numbers xj flawed”

There is no doubt about it, when you consider assigning invented weights to a relationship

5- Page 5 “Furthermore, affine measurement of preference cannot be performed through pair wise comparisons”

Obvious. Pair-wise comparisons is a measure of intuitive estimates without any foundation.

6- Page 6 “This is akin to saying that rank reversal can be avoided by measuring in kilometers instead of miles”

Agreed

7- Page 6 “This erroneous conclusion is based on his claim that the flaw is that rank reversal is a symptom of arbitrary rankings”

This claim is absurd. RR is not phenomenon in a system, it is a logical occurrence when alternatives are added or deleted, and this is due to geometrical properties

8- Page 6 “Of course, no methodology should be considered valid unless it is fully understood”

It is difficult to understand or rationalised AHP features. It is a system built on assumptions that after 70 years nobody could justify because they do not have the most elemental mathematical support and also violating common sense.

These are my comments

Nolberto Munier