[PLUG] Matrix manipulation code in C or FORTRAN

[Rich Shepard]

On Wed, 8 Oct 2003, Grigsby, Garl wrote:

> So what is it you are attempting to calculate EigenValues for, if you
> don't mind me asking? It is so rare for me to run into people in a
> non-work setting that have ever heard of an eigenvalue, much less want to
> calculate one.

Garl,

  Sorry to disappoint, but this is work related ... for me.

  I have two related applications: ranking alternatives that are not equally
attractive and as part of a multiobjective, multicriteria decision support
system under conditions of uncertainty.

  In the first application, one has the stakeholders or decision makers do a
binary pair-wise comparison of all alternative combinations: of the two,
which is preferred. Then the amount of preference is scored on a ratio scale
of 1-9. The preference is placed in a matrix of alternatives for each paired
comparison. The eigenvalue of the matrix is found and the associated
eigenvector is generated. This represents the rank of each alternative. The
eigenvector values can then be multiplied by the number of alternatives to
normalize them to the problem size.

  In the second application, a similar process is used to produce exponents
for fuzzy sets that are then aggregated using an ordered, weighted average
(OWA) set operation. Because the pair-wise values are generated for both the
objectives and the criteria (constraints), they can be used to prioritize
alternatives.

  All of this is explained in the book I'm writing and incorporated into the
fuzzy system/approximate reasoning modeling system I'm developing for
environmental impact assessments.

Rich

Dr. Richard B. Shepard, President

                       Applied Ecosystem Services, Inc. (TM)
            2404 SW 22nd Street | Troutdale, OR 97060-1247 | U.S.A.
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