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where the satisfying sample set is defined as
Z
ω
(
R
i
)=
{
z
l
∈
Z
N
,
s
.
t
.R
i
(
z
l
)
≥
ω
}
.
Covering Ratio of Dissatisfying Samples (CRDS)
TheCRDSisdefinedasfollows:
⎧
⎨
if
n
R
i
≤
n
ω
(
R
i
)
1
k
·
1
g
n
(
R
i
)=
(4)
n
ω
(
R
i
)+exp(1)
,
otherwise
⎩
n
R
i
−
k
·
where the dissatisfying sample set is described as
Z
−
(
R
i
)
{
z
l
∈
Z
N
,
s
.
t
.R
i
(
z
l
)=
0AND
A
i
(
x
l
)
>
0
}
,
A
i
(
·
)is the covering degree of
x
l
for the premises of
R
i
,
n
R
i
=
is the number of dissatisfying samples,
n
ω
(
R
i
)isthenumberof
satisfying samples,
k
is an satisfying degree of the users.
As is seen in the formulas (2)-(4), the proper covering degree for the ordinary
and the good samples is guaranteed by the indexes (2)and(3), respectively. Ad-
ditionally, the suitable covering degree for the bad examples is also considered in
the formula (4). Therefore the consistency factors among the rules are included
effectively.
GNP is denoted
LNIR
(
Z
−
(
R
i
)
|
|
·
) and described as follows:
LNIR
(
R
i
)=1
−
NIR
(
R
i
)
(5)
NIR
(
R
i
)=
Max
i
{
h
i
}
(6)
h
i
=
∗
(
A
(
N
i
x
)
,B
(
N
i
y
))
(7)
(
A
1
(
N
i
x
1
)
,...,A
n
(
N
i
x
p
))
A
(
N
i
x
)=
∗
(8)
where
R
i
:IF
x
1
is
A
1
AND
···
AND
x
p
is
A
p
THEN
y
i
is
B
i
is the adjusting
rule in each iteration;
x
j
is the
j
th input;
A
j
is the
j
th fuzzy set in
R
i
;
y
i
is
i
th
output;
B
i
is the membership function in the consequences of
R
i
;
i
=1
,...,n
is the number of rules;
j
=1
,...,p
is the dimension of the input;
Max
{·}
is
the maximum operator;
∗
is the minimum operator;
N
i
=(
N
i
x,N
i
y
)isthe
membership center of
R
i
.
Since the GNP index ranges from 0 to 1. So when there is no superposition
k
=1
i−
1
between
R
i
and the current rule set
R
k
,
LNIR
(
R
i
)is1.Orelse,
LNIR
(
R
i
)
is 0. By the search for classic centers of rules, the overlapping of fuzzy sets is
reduced.
Summarily, the fitness function is designed as follows:
F
(
R
i
)=
Ψ
Z
N
(
R
i
)
·
G
w
(
R
i
)
·
g
n
(
R
i
)
·
LNIR
(
R
i
)
(9)
4
Description of EOCA-IFIM Algorithm
In a summary, the EOCA-IFIM algorithm is described as follows:
Step 1.
Determine the number of clustering
c
and the initial centers of clusters
V
0
by EOCA;
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