John Randall wrote:
Tarmo:
Thanks for the explanation. I guess I still do not get the reliance today
on a rule of thumb method to approximate eigenvalues when there has been
technology to do it accurately for many years.
- The power method and similar iterative methods are easy to program.
- Engineers have calculated eigenvalues on computers since the 1950s.
- The routines that later were incorporated into EISPACK (and then LAPACK)
were originally written in ALGOL in 1971.
- IMSL and NAG have been going since the early 1970s.
- Maple started in 1980.
- MATLAB and Mathematica started in 1985.
Where have you guys been?
I'm afraid I wasn't even born yet when Saaty first postulated his AHP
principles (around 1973).
The power method is known in the AHP circles for a long time, but the
use of simple first iteration has persisted, especially as a teaching
example. AHP has mostly been marketed in social sciences and towards
management. I think that is the reason why the teaching material has
been kept as simple as possible. And as I said before, if the pairwise
comparisons have been made by people, then the differences (exact /
inexact, left/right) are usually perceived to be so small that the
results are more sensitive to subjective judgements (or missing
criteria) than to choosing the right eigenvector method. With subjective
judgements AHP is not an exact science. If the pairwise comparisons are
based on objective data that has been transformed to the relative scale,
then the precision is more important.
Compared to BOGSAT decision process (bunch of old guys/gals sitting
around the table - kind of like king Arthur's roundtable or the
veetshe/senate of Novgorod), AHP or any multicriteria decision making
process is a success.
There are 5 sources of information that I would recommend:
www.expertchoice.com
www.superdecisions.com
http://www.creativedecisions.net/
http://mdm.gwu.edu/Forman/
Web-HIPRE:
http://www.hipre.hut.fi/
With best wishes,
Tarmo
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