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{
,
,
,
,
}
and the scores of
LF
of the (supposedly) five students
1
2
3
4
5
in the class,
given by
μ
LF
=
0
|
1
+
0
|
2
+
0
.
75
|
3
+
1
|
4
+
0
.
5
|
5
,
it is
|
μ
L
|=
1
+
0
.
75
+
0
.
5
=
2
.
25, and
t
=
μ
A
3
(
2
.
25
)
=
2
.
25
−
2
=
0
.
25
,
since the equation of the line joining the points
(
2
,
0
)
and
(
3
,
1
)
, in the figure of
μ
A
3
,
is
y
=
x
−
2.
6.4.1 Quantified Fuzzy Statements
Another, more general, kind of quantified fuzzy statements, is
There are
Q
∈
X
,
such that “
F
1
(
x
)
is
P
1
”
,...,
“
F
n
(
x
)
is
P
n
”
,
with
X
the universe of discourse,
F
i
:
X
ₒ
F
i
(
X
)
ↂ R
,
1
≤
i
≤
n
, and
P
i
a
predicate in
F
i
(
X
),
1
≤
i
≤
n
. For example,
There are about 6 employees in the company that are young and whose
computer skills are high.
where
X
={
x
1
,...,
x
n
}
is the set of employees,
Q
=
about 6,
F
1
=
age, and
F
2
=
computer skills. These statement can be compressed to the form
There are
QH
1
's
H
2
's
≡
There are
Q
(
H
1
and
H
2
),
with
H
1
(
x
)
=
μ
P
1
(
H
1
(
x
)),
H
2
(
x
)
=
μ
P
2
(
H
2
(
x
))
, for all
x
∈
X
, and that correspond
with the rewritting:
There are about 6 employees that are young and with high computer skills,
H
2
|=
i
=
1
min
of the given statement. Finally, with
Z
=|
H
1
∩
(μ
P
1
(
F
1
(
x
i
)),
μ
P
2
(
F
2
(
x
i
)))
, and
Q
(
Z
)
=
Q
(
|
H
1
∩
H
2
|
)
, results the more compressed form
Z
is
Q
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