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The strict relation “inclusion about dimension”, when the IMFE-elements of
both matrices are elements of
x
,is
F
A
⊂
d
B
iff
(((
K
⊂
P
)
&
(
L
⊂
Q
))
∨
((
K
⊆
P
)
&
(
L
⊂
Q
))
∨
((
K
⊂
P
)
&
(
L
⊆
Q
)))
&
(
∀
k
∈
K
)(
∀
l
∈
L
)(
∀
a
∈
X)(
f
k
,
l
(
a
)
=
g
k
,
l
(
a
)).
The strict relation “inclusion about dimension”, when the IMFE-elements of
both matrices are elements not only of
x
,is
F
A
⊂
d
B
iff
(((
K
⊂
P
)
&
(
L
⊂
Q
))
∨
((
K
⊆
P
)
&
(
L
⊂
Q
))
∨
((
K
⊂
P
)
&
(
L
⊆
Q
)))
&
(
∀
k
∈
K
)(
∀
l
∈
L
)(ν(
f
k
,
l
)
=
ν(g
k
,
l
))
&
(
∀
a
1
,...,
a
)
∈
X)(
f
k
,
l
(
a
1
,...,
a
)
)
=
g
k
,
l
(
a
1
,...,
a
)
)).
ν(
f
k
,
l
ν(
f
k
,
l
ν(
f
k
,
l
The non-strict relation “inclusion about dimension”, when the IMFE-elements
of both matrices are elements of
1
F
x
,is
A
⊆
d
B
iff
(
K
⊆
P
)
&
(
L
⊆
Q
)
&
(
∀
k
∈
K
)(
∀
l
∈
L
)(
∀
a
∈
X)
(
f
k
,
l
(
a
)
=
g
k
,
l
(
a
)).
The non-strict relation “inclusion about dimension”, when the IMFE-elements
of both matrices are elements not only of
x
,is
F
A
⊆
d
B
iff
(
K
⊆
P
)
&
(
L
⊆
Q
)
&
(
∀
k
∈
K
)(
∀
l
∈
L
)(ν(
f
k
,
l
)
=
ν(g
k
,
l
))
&
(
∀
a
1
,...,
a
f
k
,
l
)
∈
X)(
f
k
,
l
(
a
1
,...,
a
f
k
,
l
)
)
=
g
k
,
l
(
a
1
,...,
a
f
k
,
l
)
)).
ν(
ν(
ν(
The strict relation “inclusion about value”, when the IMFE-elements of both
matrices are elements of
x
,is
F
A
⊂
v
B
iff
(
K
=
P
)
&
(
L
=
Q
)
&
(
∀
k
∈
K
)(
∀
l
∈
L
)(
∀
a
∈
X)
(
f
k
,
l
(
a
)<g
k
,
l
(
a
)).
The strict relation “inclusion about value”, when the IMFE-elements of both
matrices are elements not only of
1
F
x
,is
A
⊂
v
B
iff
(
K
=
P
)
&
(
L
=
Q
)
&
(
∀
k
∈
K
)(
∀
l
∈
L
)(ν(
f
k
,
l
)
=
ν(g
k
,
l
))
&
(
∀
a
1
,...,
a
ν(
f
k
,
l
)
∈
X)(
f
k
,
l
(
a
1
,...,
a
ν(
f
k
,
l
)
)<g
k
,
l
(
a
1
,...,
a
ν(
f
k
,
l
)
)).
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