Dear Djilali

It depends on the number of alternatives

Research shows that up to three alternatives both methods coincide, but not after

In my opinion, the fact that the DM must adjust his preferences because a formula says so, is absurd, especially when reality is most often no transitive, and he has to do so because if not the Eigenvalue method is not applicable.

I believe that the DM must work with whatever the inconsistence might be, and then using the geo method.

If you are interested in this subject I suggest to read the Book by Evangelos Triantaphyllou, ' Decision Making: A comparative analysis', where it is analyzed in depth

Dear Munier

thank you for your responds

I read the section 4.2 the Eigenvalue Approach in the book that you suggested and still have ambiguity.

please give me your email of course if you don't mind. I'll send to you the word file that I wrote about the method that I used.

Dear Djilali

My email address is: [email protected]

I am looking forward, and interested, for your work, Thanks

Dear Djilali

I am not a mathematician; therefore, I may only express my opinions. I believe that the Triantaphyllou book just explain the problem, and it coincides with what Theo Dijsktra says, that it is still, and after decades subject to hot debate.

One thing that in my opinion must be taken into account, and also supported by other scientists, is that for number of alternatives greater that 4, the values corresponding to both the Eigen method and the geo method diverge, also supported by Theo. Therefore, if I worked with AHP (which I don’t) I would use the geometric mean.

I really wonder why Saaty chose the Eigen method to find the priorities vector, when the geo method can be nicely do the job.

The problem as I see it is that the Eigen method demands a perfect transitivity or consistency in the decision matrix, and that small corrections made by the DM to adjust his/her preferences to a maximum of 0.10.

When inconsistencies are larger apparently the Eigen method can’t be applied.

Again, in my opinion I believe that the DM should forget about the Eigen method, and apply the geometric average and using the values obtained by his/her preferences as they are even with larger inconsistencies.

I have expressed several times in RG, and strange enough, nobody refuted me, that in my opinion the pair-wise comparison system used in AHP is absurd. The DM works on a universe of his own that he believes replicates reality. When he prepares his matrix of preferences and looks for inconsistencies he is controlling his own preferences and trying to adjust them to a consistency less that 0.10. This is for me another incongruence since he is correcting his prior estimates, done in good faith based in expertise and knowledge, on what an algebraic formula indicates.

However, worse than that, and for me hard to understand, is that he is looking for a transitive that normally does not exist in the reality he tries to emulate. Another absurdity for me is that he is able to say that A es better a certain number of times than B. A person can say, and it is legitimate, that a football team A is better than B, pero what he cannot say, at least responsibly is that A is say 3.5 times than B.

I would like somebody in RG to comment about this, and of course refute me, if he/she considers that what I say is incorrect.

Dear Dijkstra

thank you for your responds and the the article's name.

Dear Munier

thank you again for your exciting intervention

I agree with you when you said that > I find that not logical when you adjust the matrix until you get consistency less than 0.10. I find myself adjust on the expertise's opinion. and when you talk about scale you can use one of methods that mentioned below:

1 = standard linear scale 1 to 9

2 = logarithmic

3 = Square root

4 = Invers linear

5 = Balanced

6 = Power

7 = Geometric

Yes, I would use the geometrical scale.