Information Technology Reference
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∈
−{
k
f
}
∈
and for each k
i
K
and for each y
Q
,
d
k
i
,
y
=
a
k
i
,
l
g
.
Theorem 11
Let A
=[
K
,
L
,
{
a
k
i
,
l
j
}]
be an IM and let a
k
f
,
l
g
=[
P
,
Q
,
{
b
p
r
,
q
s
}]
be
its element. Then
A
|
(
a
k
f
,
l
g
)
=
A
l
g
)
⊕
a
k
f
,
l
g
,
(
k
f
,
|
∗
(
a
k
f
,
l
g
)
=
A
(
k
f
,
l
g
)
⊕
a
k
f
,
l
g
⊕[
,
−{
l
g
}
,
{
c
x
,
l
j
}] ⊕ [
−{
k
f
}
,
,
{
d
k
i
,
y
}]
,
A
P
L
K
Q
where for each x
∈
P and for each l
j
∈
L
−{
l
g
}
,
c
x
,
l
j
=
a
k
f
,
l
j
and for each k
i
∈
K
−{
k
f
}
and for each y
∈
Q
,
d
k
i
,
y
=
a
k
i
,
l
g
.
Now, we can see that the newly introduced types of IMs, namely, IFIMs, EIFIMs,
TIFIMs and ETIFIMs can be represented as EIMs, too. Indeed, if we put
I
=
I
×[
0
,
1
]×[
0
,
1
]
and
X
=
X
×[
0
,
1
]×[
0
,
1
]
,
then we directly see that the IFIMs and EIFIMs can be represented as EIMs, while,
for the sets
I
=
I
×[
0
,
1
]×[
0
,
1
]×
T
and
X
=
X
×[
0
,
1
]×[
0
,
1
]×
T ,
the TIFIMs and ETIFIMs can be represented as sets of EIMs.
3.5 New Operations Over EIMs
Now, we introduce some new (non-standard) operations over EIMs.
Let index set
I
and set
X
be fixed and let the EIMs
A
1
,
A
2
,...,
A
n
over both
sets be given.
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