Priorities derivation difference with Saaty's publication

[RP87]

Priorities derivation difference with Saaty's publication

[gluc]

@RP87 : Hmm, unfortunately I have no access to the paper. I did double check though, and I can confirm your results. I did check 2 things, though:

• I ran the same problem with the pmr package, using the ahp function. The results are very comparable to the ones from the ahp package
• I re-calculated some problems from public sources, e.g. the Car Example on Wikipedia, and again the results are the same

To be completely honest with you, I'm far from being the ultimate capacity in the field, so any feedback from the community is more than welcome.

[RP87]

Hi,
I'm myself no maths star. But I suppose will improve while digging into this.

It troubles me that you confirmed my results with the previously proposed matrix.
On my side I checked wikipedia's case (here below) and thought the issue was from my ahp (and dependencies) installation. But then you should have get a different result from mine on Saaty's example.

> cost = c(1,3,3,7)
> safety = c(1.0/3,1,1,9)
> capacity = c(1.0/3,1,1,7)
> style = c(1.0/7,1.0/9,1.0/7,1)
> mat = data.frame(cost,safety,capacity,style)
> PrioritiesFromPairwiseMatrixEigenvalues(mat, allowedConsistency = 1)
$priority
        1         2         3         4
0.0561392 0.1148294 0.1201882 0.7088432

$consistency
[1] 0.07379078

> PrioritiesFromPairwiseMatrixMeanNormalization(mat)
$priority
[1] 0.05970684 0.12230233 0.12798415 0.69000668

$consistency
[1] NA

> PrioritiesFromPairwiseMatrixGeometricMean(mat)
$priority
[1] 0.05455313 0.11678162 0.12435425 0.70431100

$consistency
[1] NA

I also looked at the pmr documentation and something puzzles me in the arguments :

dset
an “A” matrix. It should be a square matrix with diagonal values equal 1 and $a_ij = 1/a_ij$.
It has no interaction with the current divergent results (this condition is ok with the example from table 3 in Saaty's publication) but it could be an issue for me when a_ij != 1/a_ij. (ex : 4 vs 1/5 instead of 1/4).

I'll send you a spreadsheet with alternative checking.

CU
Rudy

[gluc]

Hi, I only have little time to check today, but I think you have your matrix transposed, because the data.frame will assemble by column. Try this instead:

cost = c(1,3,3,7)
safety = c(1.0/3,1,1,9)
capacity = c(1.0/3,1,1,7)
style = c(1.0/7,1.0/9,1.0/7,1)
nms <- c("cost", "safety", "capacity", "style")
mat <- matrix(c(cost, safety, capacity, style), nrow = 4, byrow = TRUE, dimnames = list(nms, nms))

PrioritiesFromPairwiseMatrixEigenvalues(mat)

And you should get:

$priority
      cost     safety   capacity      style 
0.51007502 0.23435219 0.21505404 0.04051875 

$consistency
[1] 0.07379078

[RP87]

You nailed it.

It was the use of data.frame that puts data in column.

Thanks.