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y
y
y
μ
Q
∗
(
)
=
(
(
.
,
−
10
),
(
.
,
10
))
=
(
.
,
(
−
10
,
Then,
y
max
min
0
5
1
min
0
5
max
0
5
min
1
y
y
y
10
))
=
.
,
(
−
10
,
10
)
.
0
5
since min
1
0
5.
Theareabelow
μ
Q
∗
(
y
)
=
0
.
5, is
A
=
0
.
5
×
10
=
5 square units. Hence, a way to
defuzzify
μ
Q
∗
consists of searching the center of area
, that is, a point
y
0
∈[
0
,
10
]
such that
y
0
y
0
A
2
=
0
.
5
dy
=
2
.
5, or
dy
=
5
.
0
0
y
0
0
Hence,
[
y
]
=
y
0
=
5. The defuzzified value corresponding to
x
0
=
0
.
5, is
y
0
=
5
.
The method, when the conditional is Mamdani, is graphically reflected as follows.
2nd Example.
Identical to the first example, but with the input
x
0
=
0
.
3. It is
y
10
), μ
Q
2
(
y
10
).
μ
Q
1
(
y
)
=
min
(
0
.
3
,
1
−
y
)
=
min
(
1
−
0
.
3
,
Hence,
⊨
0
.
3
,
if 0
y
3
y
10
,
μ
Q
∗
(
y
)
=
if 3
y
7
⊩
0
.
7
,
if 7
y
10
that is graphically find as follows:
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