Page 272 - Practical Design Ships and Floating Structures

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They can be regarded as .. level of belonging to u, ( i= I, 2, .... m ) ... the weighting set can be written
as:
A= ai / ui + a2 /u2 + ... + a, /urn (i= I, 2, .... m ) (5)
4) Fuzzy assessment of a single factor:
lfwe carry out an assessment with u, (i= I, 2. m) within the assessed objectives and the membership
degree of iih element y/ is r, , and then assessed set can be written as follows on the basis of the
assessed results with rth factor u, (i= I, 2, .... rn ):

r ," ivn
R, = ril /vl + r ,2 /v2 + .e.+
Obviously, it is a fi~zzy sub-set in the selected set and is written as:

Ri = ( rii , r,2 ..... r In )
Thus, we can obtain a matrix consisting of the membership degree with a single factor:
....... rln 1
rrll TlZ..
R= I ..................... r2" I I I
.......
- I r21 rZ2..
1
lrml rm2 ***--*rmn
Therefore the single factor set is also written as:

R,= r,l /(u,, vI)+ r,2 /(u,, va )A ... + rIn /(u,, v, ) (i= 1,2, .... m;J= 1, 2, .... n) (9)
in which, ( u,, v, ) is the element of direct product set U x V and v, is the grade of reasonable
relationship between u, and v,.

5) Comprehensive Fuzzy Assessment (CFA)
The sum of the elements in individual column in formula (8) is used to show the comprehensive
effective of all factors, which is as follows:
m
Rj= Cr, (j= 1,2 ..... n) (1 0)
,=I
If matrix k in the above formula (8) is multiplied by the weighting set A, then the obtained results can
reflect the comprehensive effective of all factors, the procedure shows as follows:
-.
B= AoR
The detail of the above procedure is:

I r21r22 ......... rZn 1 I
....
B = (m., a2,, .....................
am), l

(j = 1,2, .... n)