Information Technology Reference
In-Depth Information
L
σ
Only the
I
th output depends of the
JI
parameter, thus,
∂
h
i
∂
σ
JI
=
=
.
0f
i
I
(2.24)
L
Developing the partial derivative of (
2.23
), and considering (
2.24
):
M
I
l
1
w
l
I
a
l
jI
∂
σ
M
I
l
1
w
l
I
M
I
l
1
w
l
I
a
l
jI
M
I
l
∂
∂
l
=
1
M
I
l
=
1
M
I
=
=
=
w
l
I
−
w
l
I
a
l
jI
∂
1
w
l
I
L
JI
L
JI
∂
σ
=
(2.25)
=
.
M
I
l
1
w
l
I
2
L
JI
∂
σ
=
L
Given that
σ
JI
is only present in
L
rule of
I
th output, is easy to deduce that
M
I
l
=
1
w
l
I
a
l
jI
∂
σ
∂
w
I
∂
σ
∂
a
jI
=
(2.26)
L
JI
L
JI
and working in a similar way,
M
I
l
=
1
w
l
I
∂
w
I
∂
σ
∂
=
JI
.
(2.27)
L
JI
L
∂
σ
Replacing (
2.26
) and (
2.27
)in(
2.25
):
M
I
l
1
w
l
I
a
l
jI
M
I
l
⎛
⎞
=
∂
a
jI
M
I
1
w
l
I
−
M
I
1
w
l
I
a
l
jI
1
w
l
I
w
I
∂
σ
∂
⎝
⎠
l
=
l
=
=
=
M
I
l
1
w
l
I
2
L
JI
L
JI
∂
σ
=
⎛
⎝
⎞
⎠
.
M
I
l
1
w
l
I
(
a
jI
−
a
l
jI
)
w
I
∂
σ
∂
=
=
(2.28)
M
I
l
1
w
l
I
2
L
JI
=
Replacing the above expression in (
2.23
), the final expression is obtained:
⎧
⎨
⎛
⎝
⎞
⎠
˜
M
I
l
1
w
l
I
(
a
jI
−
a
l
jI
)
w
I
∂
σ
∂
j
=
0
n
=
h
i
∂
σ
∂
x
j
if
i
=
I
M
I
l
1
w
l
I
2
JI
=
L
JI
.
(2.29)
⎩
=
0
if
i
=
I
Finally, to conclude the calculation of (
2.29
) is necessary to determine the deriva-
tive of the degree of activation from the rules of the TS fuzzy model,
w
i
, with respect
Search WWH ::
Custom Search