Information Technology Reference
In-Depth Information
Chapter 6
Three Dimensional IMs
6.1 Definition of a Three Dimensional IMs
The TIFIMs, ETIFIMs and IMFEs show the necessity for definition of the concept
of a three dimensional IM (3D-IM).
Let
I
be a fixed set of indices and
X
be a fixed set of objects. Following [21], we
call “3D-IM"with index sets
K
,
L
and
H
(
K
,
L
,
H
⊂
I
) the object:
[
K
,
L
,
H
,
{
a
k
i
,
l
j
,
h
g
}]
⎧
⎨
⎫
⎬
h
g
l
1
...
l
j
...
l
n
.
h
g
∈
...
k
1
a
k
1
,
l
1
,
h
g
a
k
1
,
l
j
,
h
g
a
k
1
,
l
n
,
h
g
≡
H
.
.
.
.
.
.
⎩
⎭
...
...
k
m
a
k
m
,
l
1
,
h
g
...
a
k
m
,
l
j
,
h
g
...
a
k
m
,
l
n
,
h
g
⎧
⎨
...
...
h
1
l
1
l
j
l
n
.
k
1
a
k
1
,
l
1
,
h
1
a
k
1
,
l
j
,
h
1
...
a
k
1
,
l
n
,
h
1
≡
,
.
.
.
.
.
⎩
. . .
...
k
m
a
k
m
,
l
1
,
h
1
...
a
k
m
,
l
j
,
h
1
...
a
k
m
,
l
n
,
h
1
h
2
l
1
...
l
j
...
l
n
.
k
1
a
k
1
,
l
1
,
h
2
a
k
1
,
l
j
,
h
2
...
a
k
1
,
l
n
,
h
2
,
.
.
.
.
.
...
. . .
...
...
k
m
a
k
m
,
l
1
,
h
2
a
k
m
,
l
j
,
h
2
a
k
m
,
l
n
,
h
2
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