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xy
1
4111
43 0 1
43
−
x
0
=
=
x
+
2
y
−
43
⇒
y
=
,
2
43
−
42
2
hence,
μ(
42
)
=
=
0
.
5. The possibility of “
Age
(
p
)
42” is 0
.
5, and its
necessity is 0.
•
ˀ
μ
(
Age
(
p
)
40
)
=
ˀ
μ
(
[
0
,
40
]
)
=
μ(
40
)
=
1, and
N
ˀ
μ
(
Age
(
p
)
40
)
=
N
ˀ
μ
(
[
0
,
40
]
)
=
1
−
ˀ
μ
((
40
,
100
]
)
=
1
−
Sup
x
∈
(
μ(
x
)
=
1
−
μ(
40
)
=
0.
40
,
100
]
(
)
The possibility of “
Age
p
42” is 1, and its necessity is 0.
•
ˀ
μ
(
(
)
)
=
ˀ
μ
(
[
,
]
)
=
1, and
N
ˀ
μ
(
(
)
)
=
Age
p
33
33
100
Age
p
33
N
ˀ
μ
(
[
33
,
100
]
)
=
1
−
ˀ
μ
(
[
0
,
33
))
=
1
−
μ(
33
)
. This value can be computed by:
xy
1
32 0 1
37 1 1
x
−
32
1
5
.
0
=
=−
x
+
5
y
+
32
⇒
y
=
, and
μ(
33
)
=
5
1
5
4
That is,
N
ˀ
μ
(
Age
(
p
)
33
)
=
1
−
=
5
. The possibility of “
Age
(
p
)
33” is
1, and its necessity is 0
.
8.
Example 7.6.2
It is only known that a function
F
:
X
ₒ[
0
,
1
]
doesn't take any
value below 1
4. What can be said on the possibility and
necessity of the imprecise statements “
Fissmall
”, and “
F is not small
”?
/
4 but takes values above 3
/
Solution
The available but incomplete information can be translated by the possibility
distribution
μ
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