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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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