Civil Engineering Reference
In-Depth Information
Tabl e 1
School leaders leisure activity indicators of fuzzy weight
Leisure
Exercise/games
Art/music
Entertainment/tourism
Religion
activity
(w ; (1,2,3,4,5))
(w ; (1,2,3,4,5))
(w ; (1,2,3,4,5))
(w ; (1,2,3,4,5))
μ
(
X
,
Y
)
,
(.4; (0,0,0,.5,.5))
(.3;(0,0,.5,.5,0))
(.2;(0,0,1,0,0))
(.1;(0,0,.8,.2,0))
U
,
A
μ
(
X
,
Y
)
,
(.1; (.8,.2,0,0,0))
(.1;(0,0,1,0,0))
(0;(0,0,0,1,0))
(.8;(0,.0,0,.4,.6))
U
,
B
μ
(
X
,
Y
)
,
(.2;(.4,.4,,.2,0))
(.2;(0,0,0,.5,.5))
(.5;(0,0,.8,.2,0))
(0;(0,0,1,0,0))
U
,
B
Fuzzy mean
(.37;(.4,.2,0,.23,.17))
(.2;(0,0,.5,.33,.17))
(.23;(0,0,.6,.4,0))
(.3;(1,0,.6,.2,.2))
Index of individual leisure activities is as follows:
k
i
=
1
(
S
i
)
μ
i
(
x
)
,
ILA
=
where
is the sample for weight and memberships (degree of satisfactory of
the linguistic variables),
S
i
=
(
x
i
,
y
i
)
1
m
j
=
1
j
1
m
j
=
1
m
j
=
1
j
{
[
∑
·
μ
j
(
y
i
)+
(
∑
μ
j
(
y
j
)
·|
j
−
∑
·
m
−
1
m
−
1
μ
j
(
y
i
)
|
)]
−
1
}
is the degree of satisfactory for factors in the universe domain,
μ
j
(
x
i
)
is the weight of the factor
j
.
In order to find the general index of leisure activities for a population, we just
calculate the mean of the sample
ILA
through population, that is, general leisure
activities:
n
i
=
1
ILA
i
.
From the above definition we can find that 0
1
n
GILA
=
≤
ILA
≤
1
,
0
≤
T
ILA
≤
1
.
Example 3.1.
Suppose there are three principles doing the survey. They are asked
to write down the weight as well as the degree of satisfactory based on the factors
of the discussion domain. Table
1
shows the result.
3.2
Integrated Evaluation and Decision-Making
Since it is difficult to meet the common agreement for the supply and demand sides,
in order to minimize the gap, we would like to propose an appropriate decision rule
for the index of leisure activities.
The reason we choose geometric average with endpoints cross production is to
avoid people's unusual estimation in the lost evaluation as well as the intelligent
capital. The advantage of this estimation is that we can use this two evaluated
interval to reach an appropriate (common agreement) interval so that both sides
of people would like to accept the result, while most traditional evaluation methods
are based on the real value operation with the mean (arithmetic average) functions.
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