Civil Engineering Reference
In-Depth Information
Therefore, the rule-base of the community college course supply and demand
model is set up as below:
Rule 1: If
|
Demand
−
Supply
|≤
0
.
1, we will maintain the courses or objects.
Rule 2: If 0
.
1
≤|
Supply
−
Demand
|≤
0
.
5, we will minutely adjust the courses.
Rule 3: If 0
.
5
≤|
Demand
−
Supply
|≤
1, we will substantially adjust the courses.
3
Fuzzy Methods
3.1
Research Process
This research establishes fuzzy decision system on community college course
management. Figure
1
represents a fuzzy decision system dynamic process of course
management in community college. Through the fuzzy rule-base of course demand
and supply, we evaluate the courses to determine whether they need to be adjusted
or not. The definition and example will be addressed in the following section.
Definition 3.1 (Fuzzy Sample Mode [Data with Multiple Values]).
Let
U
be
the universal set (a discussion domain),
L
=
L
1
,
L
2
,...
L
k
asetof
k
-linguistic
variables on
U
,and
FS
i
,
n
a sequence of random fuzzy sample on
U
.
For each sample
FS
i
, assign a linguistic variable
L
j
a normalized membership
m
ij
(
∑
i
=
1
,
2
,...
k
j
k
j
1
m
ij
=
1
)
,andlet
s
i
=
∑
1
m
ij
,
j
=
1
,
2
,...,
k
. Then, the maximum value
=
=
of
S
j
(with respect to
L
j
) is called the fuzzy mode
(
FM
)
of this sample. That is,
FM
max
1
≤
i
≤
k
S
i
.
Note:
A significant level
=
L
j
|
S
j
=
for fuzzy mode can be defined as follows: Let
U
be the
universal set (a discussion domain),
L
α
=
L
1
,
L
2
,...
L
k
asetof
k
-linguistic variables
on
U
,and
FS
i
,
n
a sequence of random fuzzy sample. For each sample
FS
i
, assign a linguistic variable
L
j
a normalized membership
m
ij
(
∑
i
=
1
,
2
,...
k
j
=
1
m
ij
=
1
)
,
n
i
=
1
I
ij
,
and let
S
j
=
∑
is
the significant level. Then, the maximum value of
S
j
(with respect to
L
j
) is called
the fuzzy mode
j
=
1
,
2
,...,
kI
ij
=
1if
m
ij
≥
α
,
I
ij
=
0if
m
ij
<
α
;
α
max
1
≤
i
≤
k
S
i
.Ifthere
are more than two sets of
L
j
that reach the conditions, we say that the fuzzy sample
has multiple common agreement.
(
FM
)
of this sample. That is,
FM
=
L
j
|
S
j
=
Definition 3.2 (Fuzzy Sample Mode [Data with Interval Values]).
Let
U
be the
universal set (a discussion domain),
L
=
L
1
,
L
2
,...
L
k
asetof
k
-linguistic variables
on
U
,and
FS
i
=[
n
be a sequence of random fuzzy
sample on
U
. For each sample, if there is an interval [
c
a
i
,
b
i
]
,
a
i
,
b
i
∈
R
,
i
=
1
,
2
,...,
d
] which is covered by
certain samples, we call these samples as a cluster. Let
MS
be the set of clusters
which contains the maximum number of sample, and then the fuzzy mode
FM
is
defined as
,
FM
=[
a
,
b
]=
[
a
i
,
b
i
|
[
a
i
,
b
i
]
⊂
MS
]
.
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