Bill Harris wrote:
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Tarmo Veskioja <[EMAIL PROTECTED]> writes:
So you need to do
CR = CI % MACI, where MACI is a mean absolute consistency index of
random matrices.
See the attached code.
I checked the code. I moved
maci_precomputed =: 1000 maci"0 (3+i.8)
behind the definition of st1, otherwise it gave an error.
I am not quite sure whether maciv should include maci_precomputed in its
definition. It could be given as an argument, in that way it is possible
to either give the precomputed values or to compute the values with
greater precision.
Then you can use something like
(cr exp) % (<:<:#exp) {maci_precomputed NB. relative consistency ratio for
exp
Don't you want one more <:?
Yes, my mistake. The other alternative would be to add three 1s to the
front of maci_precomputed:
maci_precomputed =: 1, 1, 1, 1000 maci"0 (3+i.8)
In practice there can be a matrix with two elements (2x2 matrix), so at
least one 1 in front is necessary.
The verb errt that I gave in my first letter:
errt =: 13 : '^ ((y * n) + ys +/ (- ys=. +/ y=. ^. y.)) % (2 - n=. #y.)'
NB. error weights matrix
is useful to find the judgement (assessment) that is most inconsistent
with other judgements. It is based on the relation between consistent
judgements
a(i,j) * a(j,k) * a(k,i) = 1
Each judgement is part of n-2 such triples. So the error of a judgement
is the geometric mean of the errors of these n-2 triples. These errors
are true only individually - e.g. if you want to correct the judgements
one at a time. This error weight can be an aid for the expert to
reevaluate his judgement. Note that according to AHP it is acceptable to
have inconsistent judgements and the expert does not have to change his
judgements towards the more consistent direction.
If there is no more than one pairwise comparison missing from each row
and column, then it is possible to init those missing judgements to 1
and apply error corrections on those comparison cells. The same method
can be used when there are more than 1 missing comparisons, but then it
is wise to start with those missing judgements that are alone in their
row or column.
Obviously, with missing judgements there often are no precomputed maci, especially for large matrices. Maci has to be computed by generating many random matrices, for each random matrix the same missing comparison elements have to be reset to 1 and corrected.
For precomputed maci with missing judgements see:
P. T. Harker, 1987, Incomplete pairwise comparisons in the analytic hierarchy
process, Mathematical Modelling, Volume 9/11, p.837-848.
E.H. Forman, 1990, Random indices for incomplete pairwise comparison matrices,
European Journal of Operational Research, Volume 48/1, p.153-155. (matrices up
to order 7)
W.C. Wedley, 1993, Consistency prediction for incomplete AHP matrices,
Mathematical and Computer Modelling, Volume 17/4-5, February-March 1993,
p.151-161. (matrices up to order 10)
Unfortunately I don't have those articles myself, I have only read the
abstracts.
Best wishes,
Tarmo
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