Priorities derivation difference with Saaty's publication

RP87 commented 8 years ago

Hi, I can't match the results of Saaty's publication. Decision making — the Analytic Hierarchy and Network Processes (AHP/ANP)

From the article (table 3: "Criteria weights with respect to the goal")

The following Priorities

are given for the following matrix :

1   1/5     3   1/2     5
5   1   7   1   7
1/3     1/7     1   1/4     3
2   1   4   1   7
1/5     1/7     1/3     1/7     1

In R code :

Culture = c(1,1.0/5,3,1.0/2,5)
Family = c(5,1,7,1,7)
Housing = c(1.0/3,1.0/7,1,1.0/4,3)
Job = c(2,1,4,1,7)
Transportation = c(1.0/5,1.0/7,1.0/3,1.0/7,1)

mat = data.frame(Culture,Family,Housing,Job,Transportation)

PrioritiesFromPairwiseMatrixEigenvalues(mat, allowedConsistency = 0.051)
$priority
         1          2          3          4          5
0.12655215 0.04583010 0.26119217 0.05845164 0.50797395

$consistency
[1] 0.05027572

# the consistency trigger seems all right but values for priorities are different.
# alternative priorities derivation do not bring the article's values.

> PrioritiesFromPairwiseMatrixMeanNormalization(mat)
$priority
[1] 0.13099959 0.04873300 0.26082227 0.05945257 0.49999257

$consistency
[1] NA

> PrioritiesFromPairwiseMatrixGeometricMean(mat)
$priority
[1] 0.12473441 0.04501646 0.26341235 0.06047375 0.50636303

$consistency
[1] NA

Hope the issue is on my side. Double checking would be nice.

(Ubuntu 14.04 ; Rstudio 0.98.1062 ; don't know command line to list all linked packages with versions : do not hesitate to indicate command to be run for useful further informations)

BR Rudy

gluc commented 8 years ago

@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 commented 8 years ago

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 commented 8 years ago

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 commented 8 years ago

You nailed it.

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

Thanks.

gluc / ahp

Priorities derivation difference with Saaty's publication #4