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number of fuzzy sets needed to construct the model decreases, which obviously
simplifies the rule base. The simplification, however, also results when two or
more rules are equal. Here, only one of the equal rules is to be stored in the rule
base. Hence, in the approach presented here, there is a difference between
rule
base simplification
, where the primary objective is to simplify the rules by
merging similar fuzzy sets that represent almost the similar concept and
rule base
reduction
, which may follow automatically as a result of rule base simplification.
Figure 7.5 illustrates the idea of merging similar fuzzy sets, showing both rule base
simplification and rule base reduction.
If
x
1
is ….
and
x
2
is ….
then
y
is ….
f
1
R1
B1
A1
f2
R2
A2
B2
f3
R3
A3
B3
Figure 7.5(a).
Similarity-driven rule simplification (
A
1
,
A
2
,
A
3
are compatible fuzzy sets in
Rules 1, 2 and 3; similarly
B
2
and
B
3
are compatible). Note that fuzzy set
B
1
is close to the
universal fuzzy set in Rule 1.
then
y
is ….
If
x
1
is ….
and
x
2
is ….
f
c1
Rc
Ac
f
c2
R2
Ac
Bc
Figure 7.5(b).
Similarity-driven rule simplification and rule reduction (after merging
compatible fuzzy sets
A
1
,
A
2
and
A
3
in Figure 7.5(a) to give common fuzzy set
A
c
, and
similarly merging compatible fuzzy sets
B
2
and
B
3
in Figure 7.5(a) in Rule 2 and Rule 3 to
give common fuzzy set
B
c
).
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