Information Technology Reference
In-Depth Information
First, we can construct an 3D-IM with elements—real (natural) numbers, e.g.,
with the form
M
=[
A
,
B
,
C
,
{
d
k
i
,
l
j
,
h
g
}]
⎧
⎨
⎫
⎬
C
g
B
1
...
B
j
...
B
n
.
A
1
d
A
1
,
B
1
,
C
g
d
A
1
,
B
j
,
C
g
...
d
A
1
,
B
n
,
C
g
.
.
.
.
. . .
. . .
≡
|
C
g
∈
C
.
⎩
⎭
A
i
d
A
i
,
B
1
,
C
g
d
A
i
,
B
j
,
C
g
...
d
A
i
,
B
n
,
C
g
.
.
.
.
. . .
. . .
A
m
d
A
m
,
B
1
,
C
g
...
d
A
m
,
B
j
,
C
g
...
d
A
m
,
B
n
,
C
g
where
A
={
A
1
,
A
2
,...,
A
a
}
,
B
={
B
1
,
B
2
,...,
B
b
}
,
C
={
C
1
,
C
2
,...,
C
c
}
, and
≤
≤
,
≤
≤
≤
≤
:
≥
for 1
0 is a natural number, representing
the total number of sold topics with title
A
i
in bookshop
B
j
in town
C
g
.
Second, we can modify the present IM, changing its elements
d
A
i
,
B
j
,
C
g
with the
IFPs
i
a
1
j
b
,1
g
c
d
A
i
,
B
j
,
C
g
m
A
i
,
B
j
,
C
g
,
n
A
i
,
B
j
,
C
g
,
where
m
A
i
,
B
j
,
C
g
is the quantity of sold topics from
A
i
th title, divided by the total
quantity of this topic, received in bookshop
B
j
in town
C
g
and
n
A
i
,
B
j
,
C
g
is the
quantity of the same book in the bookshop warehouse, divided by the total quantity
of this topic, as above. Therefore,
m
A
i
,
B
j
,
C
g
+
n
A
i
,
B
j
,
C
g
≤
1 and number 1
−
m
A
i
,
B
j
,
C
g
−
n
A
i
,
B
j
,
C
g
corresponds to the number of non-sold topics that stay on the
shelves in the bookshop, but are not in its warehouse. Therefore, the above standard
3D-IM is transformed to 3D-IFIM.
The example is interesting, because it is a good illustration not only of the possi-
bility to transform a standard 3D-IM to a 3D-IFIM, but on its basis we can construct
a 4D-IM or 4D-IFIM. For this aim, we add a fourth component in the IM-definition,
e.g. - finite time
T
={
T
1
,
T
2
,...,
T
t
}
. So, we obtain two new IMs with the forms
M
standart I M
=[
A
,
B
,
C
,
T
,
{
d
A
i
,
B
j
,
C
g
,
t
u
}]
and
M
IFIM
=[
A
,
B
,
C
,
T
,
{
m
A
i
,
B
j
,
C
g
,
t
u
,
n
A
i
,
B
j
,
C
g
,
t
u
}]
,
≤
≤
where for the above discussed
d
A
i
,
B
j
,
C
g
and for 1
u
t
:
d
A
i
,
B
j
,
C
g
,
t
u
is a natural
number and
is an IFP.
The example shows that the 3D-IMs can be used for describing of databases, data
warehouses and OLAP-structures. Therefore, in future, the 3D- and
n
D-IMs can
obtain real applications in information technologies.
m
A
i
,
B
j
,
C
g
,
t
u
,
n
A
i
,
B
j
,
C
g
,
t
u
Search WWH ::
Custom Search