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In-Depth Information
,
,
,...
basis of the so-called Takagi-Sugenomethods of fuzzy inference of orders 1
2
3
etc.
Example 8.2.1
In the example shown in sixth step where the output
μ
Q
∗
is obtained
through Mamdani, the area below
μ
Q
∗
is easily computed by 0
.
35
×
0
.
15
+
.
×
.
0
15
0
15
+
0
.
5
×
1
=
0
.
564. Hence, the center of area is a point
y
0
∈
(
0
,
1
)
2
such that, the areas to the left and to the right of
y
0
are equal, i.e.:
y
0
0
.
564
2
=
0
.
282
=
μ
Q
∗
(
y
)
dy
0
0
.
35
y
0
=
0
.
65
dy
+
35
(
1
−
y
)
dy
0
0
.
y
0
=
0
.
228
+
y
0
−
0
.
35
−
ydy
0
.
35
as the line joining the points (0
.
35, 0
.
65) and (0
.
5, 0
.
5) is
z
=
1
−
y
. Hence:
y
0
y
0
−
=
.
−
.
+
.
=
.
ydy
0
282
0
228
0
35
0
404
0
.
35
y
0
y
2
2
y
0
35
2
2
0
.
y
0
−
35
=
y
0
−
2
−
=
0
.
404
0
.
gives:
y
0
−
2
y
0
+
0
.
686
=
0, with positive root
y
0
=
0
.
43919.
Example 8.2.2
In the case of non-null function at two number of points
y
1
,
y
2
(a two rule system) where weighted mean is taken as the output value
y
0
:
x
1
)μ
P
12
(
x
2
2
x
1
)μ
P
22
(
x
2
)
y
0
=
μ
P
11
(
)
y
1
+
μ
P
21
(
y
2
x
1
)μ
P
12
(
x
2
)
+
μ
P
21
(
x
1
)μ
P
22
(
x
2
)
μ
P
11
(
Provided that
X
1
=
X
2
=[
0
,
1
]
,
Y
=[
0
,
10
]
,
μ
P
11
(
x
1
)
=
x
1
,
μ
P
12
(
x
2
)
=
1
−
x
2
,
4,
x
1
3 and
x
2
y
1
=
6,
μ
P
21
(
x
1
)
=
1
−
x
1
,
μ
P
22
(
x
2
)
=
x
2
,
y
2
=
=
0
.
=
0
.
7, the
calculation will be:
0
.
3
×
(
1
−
0
.
7
)
×
6
+
(
1
−
0
.
3
)
×
0
.
7
×
4
0
.
54
+
1
.
96
2
.
5
y
0
=
=
49
=
58
=
4
.
31
0
.
3
×
(
1
−
0
.
7
)
+
(
1
−
0
.
3
)
×
0
.
7
0
.
09
+
0
.
0
.
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