Information Technology Reference
In-Depth Information
(
A
÷
B
)( )
z
=
∨
(
A x
( ))
∧
B y
(
)),
∀ ∈
z
R
x
+
y
=
z
z
(
kA
)( )
z
=
A
(
),
k
≠
0,
∀ ∈
z
R
k
~
A
,
B
∈
G
∀λ
∈
(
0
Theorem
12.1
Suppose
, for
, then (A±B)
ȹ
=A
ȹ
±B
ȹ
;
B
≠
θ
,
(
kA
)
=
kA
,
k
≠
0
(A×B)
ȹ
=A
ȹ
×B
ȹ
;A
B
ȹ
=A
ȹ
B
ȹ
.
λ
λ
Note
1: From Theorem 12.1 and Definition 12.2, it is clear that suppose
~
~
~
~
~
A
,
B
∈
G
A
+
G
B
G
A
×
)
B
BA
/
∈
G
(
B
≠
θ
kA
∈
G
(
k
>
0
then
.
We will discuss the calculation about fuzzy association rules in general sense.
If there is a database
T
=
t
1
,t
2
,…,t
n
, ti denotes the ith tuple
I
=(
i
1
,i
2
,…,i
n
) is the set
of attributes,
t
j
i
k
denotes the value of the attribute ik on the jth tuple. Suppose
X
=
x
1
,x
2
,…,x
p
Y
=
y
1
,y
2
,…,y
q
are the subsets of
I
, and
X
ŝ
Y
=♠
D
=
f
x1
,f
x2
,…,f
xp
E
=
f
y1
,f
y2
,…,f
yq
f
xi
(
i
=1,2,…,
p
) is the fuzzy set in the domain
of attribute xi and
y
j
. The
degree of membership of elements of these fuzzy sets is language value. The
language value is expressed as closed positive fuzzy number with boundary or
zero fuzzy number. Suppose
ε
′
is a valve value,
α
′
is the minium rate of
support.
β
′
is the minium confidence,
ŋ
',
Ȳƪ
,
ōƪ
are closed positive fuzzy number
with boundary. The form of fuzzy association rules in general sense is “if
f
yj
(
j
=1,2,…,
q
) is the fuzzy set in the domain of attribute
X
is
D
then
”.
Suppose
Y
is
E
f
xj
(
t
i
x
j
)=
x
y
ƪ
i
=1,2,…,
n
j
=1,2,…,
p
f
yj
(
t
i
y
j
)=
y
ij
ƪ
i
=1,2,…,
n
j
ƪ
ij
are closed positive fuzzy number with boundary or
zero fuzzy number. Suppose
=1,2,…,
q
both
x
ƪ
ij
and
y
′
′
x
=
max{
x
∈
R
|
x
(
x
)
=
1
i
=
1
2
?
,
n
;
j
=
1
2
?
p
;
ij
ij
′
′
y
=
max{
x
∈
R
|
y
(
x
)
=
1
i
=
1
2
?
,
n
;
j
=
1
2
?
q
;
ij
ij
′
′
′
′
α
=
max{
x
∈
R
|
α
(
x
)
=
1
β
=
max{
x
∈
R
|
β
(
x
)
=
1
