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Update equation for parameters in output layer
f
(
(
f
(
(
ʔ
w
mn
=
ʷ
Y
m
(
(
e
n
)
V
n
))
+
j
(
e
n
)
V
n
)))
(4.17)
f
(
(
f
(
(
ʔ
w
0
n
=
ʷ
z
0
(
(
e
n
)
V
n
))
+
j
(
e
n
)
V
n
)))
(4.18)
The update equations for parameters between input and hidden layer are as follows:
z
l
ʻ
m
ʓ
m
ʾ
m
N
w
lm
=
ʔ
+
j
(4.19)
exp
2
z
l
−
lm
ʓ
m
(ʳ
m
)
+
ʾ
m
(ʳ
m
)
(4.20)
2
N
w
RB
lm
W
RB
m
w
RB
ʔ
=
−
Z
−
N
W
m
Z
T
ʓ
m
ʾ
m
ʔʻ
m
=
+
j
(4.21)
exp
2
ʓ
m
ʾ
m
N
W
RB
m
ʔʳ
m
=
−
Z
−
+
j
(4.22)
z
0
ʓ
m
ʾ
m
N
ʔ
w
0
m
=
+
j
(4.23)
N
ʓ
m
f
(
(
V
m
))
f
(
(
f
(
(
where
=
1
{
(
e
n
)
V
n
))
(
w
mn
)
+
(
e
n
)
V
n
))
(
w
mn
)
}
n
=
N
ʾ
m
f
(
(
V
m
))
f
(
(
f
(
(
and
=
1
{
(
e
n
)
V
n
))
(
w
mn
)
−
(
e
n
)
V
n
))
(
w
mn
)
}
n
=
4.3.6 Model-3
Over the years, a substantial body of evidence has grown to support the presence
of nonlinear aggregation of synaptic inputs in the neuron cells [
1
,
2
]. This section
exploit a novel fuzzy oriented averaging concept, appeared in [
35
], to design a very
general nonlinear aggregation function whose special cases appear in various types
of existing neural aggregation functions. In general, an aggregation operation can
be viewed as averaging operation [
38
]. A brief survey into the history of averaging
operations brings out the fact that in 1930 Kolmogoroff [
39
] and Nagumo [
40
]
acknowledged the family of quasi-arithmetic means as a most general averaging
operations. This family has been defined as follows:
x
n
;
ˉ
1
,ˉ
2
...ˉ
n
)
=
ˆ
−
1
n
M
ˆ
(
x
1
,
x
2
...
ˉ
k
ˆ(
x
k
)
(4.24)
k
=
0
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