Civil Engineering Reference
In-Depth Information
=[
,
]
Definition 1 (Scaling for a interval fuzzy number on R).
Let
A
a
b
be an
(
−
)
/
interval fuzzy number on U with its center
a
b
2. Then the defuzzification
ln
(
1
+
A
)
number RA of
A
=[
a
,
b
]
is defined as
RA
=
cx
+(
1
−
)
,where
A
is the
A
length of the interval.
However, there are few literatures and definitions appear on the measurement
system. In this section, a well-defined distance for interval data will be presented.
Definition 2.
Let
A
i
=[
a
i
,
b
i
](
i
=
1
,
2
,
n
)
be a sequence of interval fuzzy number on
U
with its center
(
a
−
b
)
/
2. Then the distance between the trapezoid fuzzy number
A
i
and
A
j
is defined as
ln
(
1
+
A
i
)
ln
(
1
+
A
j
)
d
(
A
i
,
a
j
)=
|
cx
i
−
cx
j
|
+
|
−
|
A
i
A
j
The traditional five-point scale used in scoring is often five options. The sequence
score from small to large is often 1, 2, 3, 4, and 5 points then to calculate the sum.
According to this principle, the scoring method also can apply in discrete type of
fuzzy numbers. It can let the distance of option value become larger, and it might
help achieve a significant level after testing.
Definition 3.
Defuzzification for discrete fuzzy data. Let
X
be a fuzzy sample on
universe domain
U
with ordered linguistic variable
L
i
;
i
=
1
,.
k
,
corresponding to
n
i
=
1
integral values,
μ
X
(
L
i
)=
m
i
be the membership with respect to
L
i
,
∑
μ
X
(
L
i
)=
1.
k
i
=
1
m
i
L
i
be the centroid of the fuzzy data and d
x
k
i
=
1
m
i
|
Let
cx
=
∑
=
∑
i
−
cx
|
be its
deviation for the
cx
. We call
X
f
=
cx
+
dx
the defuzzification value for the discrete
fuzzy sample
X
.
Example 2.2.
Let
X
=
0
/
1
+
0
.
6
/
2
+
0
.
3
/
3
+
0
.
1
/
4
+
0
/
5 be a discrete fuzzy
sample on the ordered linguistic variable
L
1
=
1
,
L
2
=
2
,
L
3
=
3
,
L
4
=
4
,
L
5
=
5.
Then the defuzzification value for the fuzzy data
X
is
k
i
=
1
m
i
L
i
+
k
i
=
1
1
2
m
i
=
|
−
|
=
.
+
.
=
.
Xf
i
cx
2
5
0
3
2
8
3
An Intergrated Fuzzy Evaluation Process
On the above-mentioned human capital measurement, we will consider new
approach of measurement. Analysis by traditional methods usually involves the
following weaknesses: (a) The use of arithmetic in traditional questionnaires
is often an over-explanation. (b) Experimental data are often overused just to
cater to the need for apparent numerical accuracy. (c) For the sake of simplifying
the evolutional model, however, will neglect the relationship of actual condition
and dynamic characteristic. We better make use of fuzzy statistical technique at
investigation realm to estimate the human resource capital.
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