Information Technology Reference
In-Depth Information
belonging to the language variable fuzzy set. Employ Gauss function as the
membership function, which is expressed as:
y
=
e
−
(
x−c
)
2
(1)
σ
2
isi
=
μ
i
=
e
−
(
x
(1
i
−c
isi
)
2
(
x
i
−
c
isi
)
2
σ
isi
I
(2)
,o
(2)
σ
isi
isi
=
−
(2)
where,
c
isi
and
o
isi
represent the center and width of the membership function.
Layer 3 (fuzzification rules layer): There are 18 nodes representing 18 fuzzy
rules used to complete the antecedent calculation of fuzzy rules. Each node
represents one fuzzy rule, which is used to match the front layer of fuzzy rules
and calculate the applicable degrees of each rule.
α
j
=
μ
s
1
1
μ
s
2
2
,s
1
j
∈
1
,
2
,...,m
1
,s
2
j
∈
1
,
2
,...,m
2
(3)
I
k
=
μ
1
μ
2
=
α
k
,o
k
=
I
k
(4)
Layer 4 (fuzzification output layer): There are 18 nodes representing 18 applica-
ble degrees of each rule. Each node is processed by normalization, and also can
be used as the output layer weights of next network layer.
α
j
N
A
,o
(4
j
=
I
(4
j
=
α
j
I
j
=
α
j
=
(5)
i
=1
α
i
Layer 5 (output layer): there is only one node representing the result of pesticide
decision.
For the fuzzy segment value of input component has been determined, the
parameters needed to learn are only the last layer of connection weights
ω
ij
(
i
=
1
,
2
,...,r
;
j
=1
,
2
,...,m
) , as well as the width
σ
ij
(
i
=1
,
2
,...,r
;
j
=1
,
2
,...,m
)
and center value
c
i
j
of the second floor of the membership functions. The error
cost function is defined as:
r
E
=
1
2
(
y
di
−y
i
)
2
(6)
i
=1
where,
y
di
and
y
i
represent the output and desired output of network separately.
BP algorithm is used to calculate
d
E
d
ω
ij
,
d
E
d
c
ij
,
d
E
d
σ
ij
, and a gradient optimiza-
tion algorithm is used to adjust
ω
ij
,
c
ij
,
σ
ij
. Finally the learning algorithms of
adjusting parameters are presented as:
β
d
E
ω
ij
(
k
+1)=
ω
ij
(
k
)
−
d
ω
ij
,j
=1
,
2
,...,m
i
(7)
β
d
E
c
ij
(
k
+1)=
c
ij
(
k
)
−
d
c
ij
,j
=1
,
2
,...,m
i
(8)
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