Civil Engineering Reference
In-Depth Information
Tabl e 2
Fuzzy evaluation
r
1
r
2
...
r
f
S
1
μ
S
1
1
μ
S
1
2
...
μ
S
1
f
S
2
μ
S
2
1
μ
S
2
2
...
μ
S
2
f
.
.
.
.
.
.
.
S
k
μ
S
k
1
μ
S
k
2
...
μ
S
k
f
Ps. r
μ
A
is the membership of
A
in utility sequence
r
3.2
Calculate Procedure of Fuzzy Relative Weight
We design Table
2
as fuzzy evaluation table to calculate fuzzy relative weight.
Let
r
1
≺
r
2
≺ ...≺
r
f
, then the fuzzy weight of factor is defined.
f
l
=
1
μ
S
1
l
/
r
l
=
μ
S
1
1
/
r
1
+
μ
S
1
2
/
r
2
+
...
+
μ
S
1
f
/
r
f
,
FW
S
1
=
f
l
=
1
μ
S
2
l
/
r
l
=
μ
S
2
1
/
r
1
+
μ
S
2
2
/
r
2
+
...
+
μ
S
2
f
/
r
f
,
FW
S
2
=
(1)
...
f
l
=
1
μ
S
k
j
/
r
l
=
μ
S
k
1
/
r
1
+
μ
S
k
2
/
r
2
+
...
+
μ
S
k
f
/
r
f
.
FW
S
k
=
Utilize the m grade evaluation criterion and calculate fuzzy relative weight FRW
of each factor. The meaning of m grade evaluation criterion is that utility
sequence
r is regarded as f grade; fetch the quantity to this f grade. That is to say, let the value
of
r
1
be one
(
r
1
=
1
)
,
r
2
be two
(
r
2
=
2
)
,andthen
r
f
be
f
(
r
f
=
f
)
.Then
f
l
=
1
l
f
l
=
1
l
f
l
=
1
l
μ
S
1
l
μ
S
2
l
μ
S
k
l
∑
∑
∑
FRW
S
1
=
μ
S
1
l
,
FRW
S
2
=
μ
S
2
l
,...,
FRW
S
k
=
f
l
=
1
l
f
l
=
1
l
f
l
=
1
l
i
i
i
μ
S
k
l
(2)
∑
∑
∑
∑
∑
∑
=
1
=
1
=
1
3.3
Strategy: Emphasize One Certain Aspect
Let
X
be the universe set,
X
X
N
,and
X
i
beavariableon
X
. The relative
importance of
X
i
is higher than the other variables. The fraction that focuses on
X
i
is viewed as
S
=
X
1
,
X
2
,...,
, and then the fuzzy multiple decisions for emphasis on a certain
aspect are defined as
(
X
i
)
n
i
=
i
,
i
=
1
X
i
n
(
∑
(
)=
)
S
X
i
X
i
(3)
−
1
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