It is now possible, to analyse the weight uncertainties in your AHP-OS projects. When you view the results (View Result from the Project Administration Menu), you see the drop-down list for different AHP scales and a tick box var is shown.
Tick var and click on Refresh. All priority vectors of your project will display the weight uncertainties with (+) and (-).
Dear Friends, dear Visitors,
over the last four months I put in a lot of effort to improve the AHP-OS online tool. With several releases a simplified menu structure and new features were introduced.
The last two features are based on my recent study about the comparisons of different AHP scales. Up to date there was no recommendation, what scales to use, and I found a new approach to analyse and compare the scales based on simple analytic functions. This study is submitted for publication, and I hope it will not take too long, until it is available. You can find some more information already in my posting here.
The feature of analysing weight uncertainties is an innovative way of doing sensitivity analysis: all judgments are randomly varied by ±0.5 on the judgment scale, and for each variation the maximum and minimum out coming priorities are captured. I use 1000 variations, enough to get a relatively stable margin of errors for each weight. It gives you information, how “precise” a weight or ranking is in your specific project.
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For now, please enjoy your visit on the site and feel free to leave a comment – it is always appreciated.
Klaus D. Goepel,
Singapore, June 2017
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As part of my current work about AHP scales, here an important finding for the balanced scale:
Salo and Hamalainen [1] pointed out that the integers from 1 to 9 yield local weights, which are not equally dispersed. Based on this observation, they proposed a balanced scale, where local weights are evenly dispersed over the weight range [0.1, 0.9]. They state that for a given set of priority vectors the corresponding ratios can be computed from the inverse relationship
r = w / (1 – w) (1a)
The priorities 0.1, 0.15, 0.2, … 0.8, 0.9 lead, for example, to the scale 1, 1.22, 1.5, 1.86, 2.33, 3.00, 4.00, 5.67 and 9.00. This scale can be computed by
wbal = 0.45 + 0.05 x (1b)
with x = 1 … 9 and
(1c)
c ( resp. 1/c) are the entry values in the decision matrix, and x the pairwise comparison judgment on the scale 1 to 9.
In fact, eq. 1a or its inverse are the special case for one selected pairwise comparison of two criteria. If we take into account the complete n x n decision matrix for n criteria, the resulting weights for one criterion, judged as x-times more important than all others, can be calculated as:
(2)
Eq. 2 simplifies to eq. 1a for n=2.
With eq. 2 we can formulate the general case for the balanced scale, resulting in evenly dispersed weights for n criteria and a judgment x with x from 1 to M:
(3)
with
(3a)
(3b)
(3c)
We get the general balanced scale (balanced-n) as
(4)
