Information Technology Reference
In-Depth Information
Sum-column-aggregation
l
0
j
=
1
n
k
1
a
k
1
,
l
j
σ
sum
(
,
l
0
)
=
,
A
.
.
j
=
1
n
k
m
a
k
m
,
l
j
Average-column-aggregation
l
0
j
=
1
n
1
n
k
1
a
k
1
,
l
j
σ
ave
(
A
,
l
0
)
=
.
.
.
j
=
1
n
1
n
k
m
a
k
m
,
l
j
We can see immediately that for every IM
A
, for every pair of indices
i
and
j
and
for every
◦∈{
max
,
min
,
sum
,
ave
}
:
(1)
ρ
◦
(ρ
◦
(
A
,
j
),
i
)
=
ρ
◦
(
A
,
i
),
(2)
σ
◦
(σ
◦
(
A
,
i
),
j
)
=
σ
◦
(
A
,
j
),
(3)
ρ
◦
(σ
◦
(
A
,
j
),
i
)
=
σ
◦
(ρ
◦
(
A
,
i
),
j
).
-IMs, only operations Max-row-, Min-row-, Max-column-
and Min-column aggregation are possible.
In the case of
(
0
,
1
)
1.3 Relations Over
R
-IM and
(
0
,
1
)
-IM
Let the two IMs
A
=[
K
,
L
,
{
a
k
,
l
}]
and
B
=[
P
,
Q
,
{
b
p
,
q
}]
be given. We shall in-
troduce the following (new) definitions where
⊂
and
⊆
denote the relations
“strong
inclusion”
and
“weak inclusion”.
The strict relation “inclusion about dimension”
is
A
⊂
d
B
iff
(((
K
⊂
P
)
&
(
L
⊂
Q
))
∨
((
K
⊆
P
)
&
(
L
⊂
Q
))
∨
((
⊂
)
(
⊆
)))
(
∀
∈
)(
∀
∈
)(
a
k
,
l
=
b
k
,
l
).
K
P
&
L
Q
&
k
K
l
L
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