Information Technology Reference
In-Depth Information
(
◦
,
∗
)
∈{
(
+
,
×
), (
,
), (
,
), . . .
}
where
.
Here we give an example. Let us have the IMs
X
and
Y
max
min
min
max
cr
cd e
a
g
1
g
2
X
=
a
f
1
f
2
f
3
f
4
f
5
f
6
,
Y
=
,
p
g
3
g
4
b
q
g
5
g
6
with elements
1
x
i
f
i
(
x
)
=
, g
i
(
x
)
=
i
.
x
1
for
i
=
1
,
2
,...,
6. Therefore, the elements of both IMFE are elements of set
F
x
.
Hence,
cder
c
de
r
1
x
x
2
x
3
2
x
a
f
1
+
g
1
f
2
f
3
g
2
a x
+
x
4
x
5
x
6
X
⊕
(
+
)
Y
=
b
f
4
f
5
f
6
⊥
=
b
⊥
1
3
x
1
4
x
p
g
3
⊥⊥
g
4
p
⊥⊥
q
g
5
⊥⊥
g
6
1
5
x
1
6
x
q
⊥⊥
1
is an IMFE with elements of set
F
x
.
1
1
On the other hand, if for
i
=
1
,
2
,...,
6:
g
i
(
y
)
=
y
, then
g
i
∈
F
y
and for the
i
.
above IMFE
X
and for the new IMFE
Y
we obtain:
cder
c
de
r
1
y
x
3
2
y
x
2
a x
+
a
f
1
+
g
1
f
2
f
3
g
2
x
4
x
5
x
6
b
⊥
X
⊕
(
+
)
Y
=
b
f
4
f
5
f
6
⊥
=
,
1
3
y
1
4
y
⊥⊥
p
g
3
⊥⊥
g
4
p
q
g
5
⊥⊥
g
6
1
5
y
1
6
y
q
⊥⊥
2
. Obviously, if
g
i
y
i.e., the IMFE
X
⊕
(
+
)
Y
∈
F
∈
F
z
, i.e., if it has two arguments
,
x
(
y
and
z
, different from
x
), then
X
⊕
(
+
)
Y
∈
F
z
. It is suitable to define for each
,
y
,
function
f
with
n
arguments:
ν(
f
)
=
n
.
5.3 Relations Over IMFEs
Let everywhere, variable
x
obtain values in set
X
(e.g.,
X
being a set of real numbers)
and let
a
be an arbitrary value of
x
.
Let the two IMFEs
A
∈
X
=[
K
,
L
,
{
f
k
,
l
}]
and
B
=[
P
,
Q
,
{
g
p
,
q
}]
be given. We intro-
duce the following definitions where
⊂
and
⊆
denote the relations “
strong inclusion
”
and “
weak inclusion
”.
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