Re: error: `eig' undefined near line 5 column 7

[Geraint Paul Bevan]

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Rich Shepard wrote:

|
|   The original matrix represents the results of pair-wise comparisons of
| components in an environmental impact assessment. There is a fixed scale
| (from 1 to 9) keyed to comparative labels such as "almost equal
importance",
| "slightly more important" and "greatly more important". The rows and
columns
| are the average values for the pair-wise comparisons. That's why the
| diagonal is 1s and why the matrix is symetrical. In the example, if
one pair
| is scored as 3.000, then the mirror cell is 0.333.
|
|   The way this is supposed to work as an Ordered Weighted Average
(OWA) when
| dealing with fuzzy logic, is that each element of the resultant
eigenvector
| is multiplied by the class of the matrix (i.e., the number of rows or
| columns; 3 in the case of the example) to provide relative weights (in the
| range [0,1]) for each component.
|
|   This is why imaginary parts to the values don't make sense in the
context
| in which the computation is to be used. Working the example by hand --
using
| an alternative to eigenvector calculation -- the numbers come out just
fine.
| Sigh.
|
| Thanks,
|
| Rich
|



Is this the same method as the Analytic Hierarchy Process (AHP)?
If so, according to [1], there are 3 criteria for a consistent comparison:

aij=wi/wj=1/aji, aii=1.0, aik·akj=aij, (i, j, k=1, 2, & n).

It doesn't look like the matrix from your book satisfies the last of
these. For i=1,j=2,k=3, for example:

(a13=1/2)*(a32=1/3) != (a12=1/3)


[1] Júlíus Sólnes, Environmental quality indexing of large industrial
development alternatives using AHP, Environmental Impact Assessment
Review, Volume 23, Issue 3, May 2003, Pages 283-303.
(http://www.sciencedirect.com/science/article/B6V9G-48CX6KS-1/2/cb6aed0fbf6f24b3ac2efad7df03fe7c)

- --
Geraint Bevan
http://homepage.ntlworld.com/geraint.bevan

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