Bill Harris wrote:
NB. Calculate the consistency ratio
n =: #
cr =: (ev - n) % <: @: n
Your cr is called the absolute consistency index (CI). What Coyle refers
to is called relative consistency ratio (CR). From Coyle's paper on page 5:
"...the calculation of a Consistency Ratio (CR) to measure how
consistent the judgements have been relative to large samples of purely
random judgements. If the CR is much in excess of 0.1 the judgements are
untrustworthy because they are too close for comfort to randomness..."
So you need to do
CR = CI % MACI, where MACI is a mean absolute consistency index of
random matrices.
Saaty and others have MACI precomputed for matrices up to size 10.
NB. MACI based on 1 000 000 random matrices
3 4 5 6 7
8 9 10
0.524500 0.884133 1.10857 1.24902 1.34039 1.40437 1.45050 1.48607
The 0.5245 for 3x3 matrices is exact.
One can use Roger's code for generating random matrices (I had to put
back the dot behind y, since I still use J5.04):
st1=: 3 : 0
i=. 1+(,~y.) [EMAIL PROTECTED] #saaty_scale
b=. >/~i.y.
((b*i) + |:b*i+#saaty_scale) { 1,(,%) saaty_scale
)
Thanks Roger for the speedup!
Then you can use something like
am =: +/ % # NB. arithmetic mean
maci =: 13 : 'am cr"2 st1"0 (x. # y.)' NB. cr =: (ev - n) % <: @: n
maci_precomputed =: 1000 maci"0 (3+i.8) NB. larger x. will
obviously give a more precise answer
(cr exp) % (<:<:#exp) {maci_precomputed NB. relative consistency
ratio for exp
NB. Results for all 4 of Coyle's 3x3 matrices
cr exp
0.014531883 NB. Coyle: 0.072
I think Coyle's CR=0.072 is a typo and it should be 0.0145319 % 0.5425 =
0.027 (actually 0.0277062).
cr und
0.014531883 NB. Coyle: 0.026
It should also be 0.0277062
cr rod
_4.4408921e_16 NB. Coyle: 0
0 considering rounding errors.
cr pod
0.00061677663 NB. Coyle: 0
0.00061677 % 0.5425
0.0011369
Bill Harris wrote:
If I get a moment, would anyone object if I pick some of the best code,
add the eigenvalue calculation, and put it on the Wiki as a Saaty
framework in J?
I don't mind. I might have some ideas to add but it is past midnight
already.
Cheers,
Tarmo
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