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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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