AI - a Guide to Intelligent Systems.pdf - Member of EEPIS

294
HYBRID INTELLIGENT SYSTEMS
Step 2:
Determine the maximum degree of compatibility of the new pattern
with each class:
h
Cn
¼ max Cn
1fA 1B 1g ;Cn 1fA 1B 2g ;Cn 1fA 2B 1g ;Cn 1fA 2B 2g; ð8:29Þ
Cn
2fA 1 B 1 g ;...;Cn 2fA 1 B Kg ;Cn 2fA 2 B 1 g ;...;Cn 2fA 2 B Kg ;...;Cn 2fA KB 1 g ;...;Cn 2fA ;...;
KB Kg
i
Cn
LfA 1 B 1 g ;...;Cn LfA 1 B Kg ;Cn LfA 2 B 1 g ;...;Cn LfA 2 B Kg ;...;Cn LfA KB 1 g ;...;Cn LfA KB Kg
n ¼ 1; 2; ...; N
Step 3:
Determine class C m with which the new pattern has the highest degree
of compatibility, that is:
Cm
¼ max C 1
; C
2
; ...; CN
ð8:30Þ
Assign pattern x ¼ðx1; x2Þ to class C m .
The number of multiple fuzzy rule tables required for an accurate pattern
classification may be quite large. Consequently, a complete set of rules S ALL can
be enormous. Meanwhile, the rules in S ALL have different classification abilities,
and thus by selecting only rules with high potential for accurate classification,
we can dramatically reduce the size of the rule set.
The problem of selecting fuzzy IF-THEN rules can be seen as a combinatorial
optimisation problem with two objectives. The first, more important, objective is
to maximise the number of correctly classified patterns; the second is to
minimise the number of rules (Ishibuchi et al., 1995). Genetic algorithms can
be applied to this problem.
In genetic algorithms, each feasible solution is treated as an individual, and
thus we need to represent a feasible set of fuzzy IF-THEN rules as a chromosome
of a fixed length. Each gene in such a chromosome should represent a fuzzy rule
in S ALL , and if we define S ALL as:
S ALL ¼ 2 2 þ 3 3 þ 4 4 þ 5 5 þ 6 6
the chromosome can be specified by a 90-bit string. Each bit in this string can
assume one of three values: 1, 1or0.
Our goal is to establish a compact set of fuzzy rules S by selecting appropriate
rules from the complete set of rules S ALL . If a particular rule belongs to set S, the
corresponding bit in the chromosome assumes value 1, but if it does not belong
to S the bit assumes value 1. Dummy rules are represented by zeros.
What is a dummy rule?
A dummy rule is generated when the consequent of this rule cannot be
determined. This is normally the case when a corresponding fuzzy subspace
has no training patterns. Dummy rules do not affect the performance of a
classification system, and thus can be excluded from rule set S.