Information Technology Reference
In-Depth Information
◦
X
=
Y
=
Z
and “
. Only in this case, the form of indices is
different: now, it is a triple of index and two numbers in
” is “max” and
[
,
]
representing the
degrees of its validity (existence, etc) and of its non-validity (non-existence, etc).
0
1
If
◦:
X
×···×
X
→
X,
the aggregation operations have the forms
◦
-row-aggregation
l
1
l
2
...
l
n
m
◦
m
◦
m
◦
ρ
◦
(
A
,
k
0
)
=
a
k
i
,
l
n
,
k
0
a
k
i
,
l
1
a
k
i
,
l
2
...
i
=
1
i
=
1
i
=
1
◦
-column-aggregation
l
0
n
◦
k
1
a
k
1
,
l
j
j
=
1
σ
◦
(
A
,
l
0
)
=
,
.
.
n
◦
j
=
1
k
m
a
k
m
,
l
j
1
will coincide with
j
=
1
.
defined over EIMs without changes.
m
j
◦
+
◦
where, as above, e.g., when
is
, the symbol
=
3.3 Relations Over EIMs
Let the two IMs
A
=[
K
,
L
,
{
a
k
,
l
}]
and
B
=[
P
,
Q
,
{
b
p
,
q
}]
be given, where
a
k
,
l
∈
X
,
b
p
,
q
∈
Y
, and
K
,
L
,
P
,
Q
⊂
I
.Let
R
s
and
R
n
be a strict and a non-strict relations
over
, respectively.
We introduce the following definitions, where
X
×
Y
⊂
and
⊆
denote the relations “
strong
inclusion
” and “
weak inclusion
” over standard sets.
The first two relations from Sect.
1.3
keep their form, while, the rest four def-
initions are valid only if there are two relations
R
s
and
R
n
—strict and non-strict,
defined over
X
×
Y
.
Then, for EIMs, the definitions for relations over EIMs obtain respectively the
forms
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