Civil Engineering Reference
In-Depth Information
[
,
]
a
b
represents an interval-type fuzzy number in which a is the lower bound of
[
,
]
[
,
]
=
[
,
]=[
,
]=[
,
]=
=
a
b
,and
b
is the upper bound of
a
b
.If
a
b
,then
a
b
a
a
b
b
a
b
(
)
represents a real number
a
or b
. Similarly, a real number
k
can be represented as
[
,
]
k
k
.
2.2
Interval Fuzzy Calculated
2.2.1
The Definition of 2.1 Continuous Fuzzy Sample Mean
Let U be a domain,
L
=
{
L
1
,
L
2
,...,
L
k
}
of K-language variables is distributed in the
domain U.
{
x
i
=[
a
i
,
b
i
]
,
i
=
1
,...,
n
}
is a set of fuzzy sample in the domain U.
Fuzzy sample mean as
1
n
i
=
1
b
i
n
i
=
1
a
i
,
n
1
n
F x
=
2.2.2
Empirical Analysis
First, the results from 13 principles to answer the questionnaires were organized,
have five categories, teaching courses, administrative tasks, public relations build-
ing, crisis management, and miscellaneous affairs, and are a group of fuzzy sample.
I
1
,
refer to the respondent ID, whereas numbers 1 and 2 in the gender field
represent male and female. Whether outstanding leadership awards have been won
is denoted by placing
a
√
in the field.
By definition 2.1 the fuzzy number of sample was calculated as follows:
I
2
,
I
3
...
0
+
1
+
1
+
1
+
1
+
1
+
1
+
1
+
0
+
1
+
2
+
2
+
3
=
,
F x
13
2
+
3
+
3
+
2
+
3
+
2
+
2
+
2
+
3
+
3
+
4
+
3
+
5
=[
1
.
2
,
2
.
8
]
HR
13
1
+
+
+
+
+
+
+
+
+
+
+
+
1
3
2
2
2
3
3
0
3
3
2
2
F x
=
,
13
4
+
3
+
5
+
4
+
3
+
3
+
5
+
5
+
3
+
5
+
5
+
3
+
6
=[
2
.
1
,
4
.
2
]
HR
13
0
+
2
+
0
+
1
+
1
+
1
+
3
+
2
+
0
+
0
+
1
+
2
+
3
F x
=
,
13
4
+
3
+
2
+
2
+
2
+
2
+
4
+
3
+
4
+
1
+
3
+
3
+
6
=[
1
.
2
,
3
]
HR
13
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