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μ
Example 7.8.3
Which is the probability of the fuzzy event
Solution
(μ)
=
[
=
[
+
[
=
4
(
+
5
(
10
·
p
]
μ
dx
]
μ
1
dx
]
μ
2
dx
4
−
x
)
dx
6
−
x
)
dx
=
0
,
10
4
,
5
5
,
6
1
3
2
−
2
+
=
1. Then
p
(μ)
=
0
.
1.
Example 7.8.4
Which is the probability of the fuzzy event
μ
:
1
σ
μ
0
1/4
3/4
1
Which is the conditional probability
p
(˃/μ)
?
Solution
(μ)
=
=
3
/
4
1
+
3
/
4
1
dx
4
+
3
/
4
1
1
1
1
4
1
p
]
μ
dx
μ
1
dx
=
4
(
2
x
−
2
)
dx
=
4
+
=
2
.
[
,
/
/
0
10
4
1
p
(˃
·
μ)
p
(μ)
=
p
(˃
|
μ)
=
2
p
(˃
·
μ)
, with
˃
·
μ
=
min
ⓦ
(˃
×
μ)
, given by
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