Using Class Decomposition for Building GA with Fuzzy Rule-Based Classifiers - Developing Concepts in Applied Intelligence - page 72

c -class problem is divided into c subproblems, each contains the vectors X i that
present T j . Hence the class set can be denoted as
T = T 1 T 2 ... T c

each subproblem can be formulated as required f j with an optimal classification
accuracy and score on T j

f j : X → T j .

Having c subproblems, c GA sub-modules are constructed and could be executed
in parallel.

2.6 Integration

Although each GA module has evolved a portion of the solution, we cannot just
simply aggregate their sub-solutions as the final one, because each GA module
only classifies only one class. Therefore, when the sub-solutions are combined
together, there may still exist conflicts among the sub-solutions. For example,
rules from different modules may classify an instance into several classes. In
order to resolve these conflicts and further improve the classification rate, the
classifier employs some intelligent decision rules. The detailed integration process
is explained as follows.
The classifier constructs an overall rule set by aggregating all rules from c
modules. Some decision rules are added to help resolve the above-mentioned
conflicts. We believe that the ending classification rate obtained from each mod-
ule would be useful for this purpose. Currently, the following decision rules have
been employed:

i) If an instance is classified into more than one class categories by the rule
set, it will be classified into the one whose corresponding module achieves the
highest classification rate in the training phase.
ii) If an instance is not classified into any class category by the rule set, it
will be classified into the class whose corresponding module achieves the lowest
classification rate in the training phase, if available.

2.7 Proposed Algorithm

To sum up, the process employed in this paper can be summarized by the fol-
lowing algorithm:
Input: Population size N; Maximum number of generations G; Crossover prob-
ability p c ; Mutation rate p m .
Output: Classifier

1. GP = φ
2. for each Class C i do
(a) P i :=Initialize(P, C i )
(b) while the termination criterion is not satisfied do