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In-Depth Information
Fig. 9.3
Architecture of ANFIS
number between 0 and 1.
w
i
=
μ
A
,
i
(
f
y
)μ
B
,
i
(
f
z
)
;
i
=
1
,...,
3
(9.2)
w
i
i
=
1
w
i
w
i
=
i
=
1
,...,
3
.
(9.3)
In the fourth layer the fuzzy sets that represent the outputs of each rule are com-
bined into a single fuzzy set.
O
4
,
i
=
w
i
z
i
;
i
=
1
,...,
3
(9.4)
which corresponds to three fuzzy if-then rules of Takagi-Sugeno type which are:
If f
y
is
μ
A
,
1
and f
z
is
μ
B
,
1
then z
1
=
p
1
f
y
+
q
1
f
z
+
r
1
(9.5)
If f
y
is
μ
A
,
2
and f
z
is
μ
B
,
2
then z
2
=
p
2
f
y
+
q
2
f
z
+
r
2
(9.6)
If f
y
is
μ
A
,
3
and f
z
is
μ
B
,
3
thenz
3
=
p
3
f
y
+
q
3
f
z
+
r
3
.
(9.7)
Finally, defuzzification process is applied in the fifth layer by weighted average
(
9.8
) where C is the damping value given as system output.
i
=
1
w
i
z
i
C
=
i
=
1
w
i
.
(9.8)
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