Information Technology Reference
In-Depth Information
Fuzzy System
Fuzzy
Rules
Genetic
Algorithm
Training data
Fuzzy Output
Variable
Fuzzy
Variables
ReRecBF
DDA/RecBF
Fig. 2.1.
Our method's schema. Solid line rectangles represent algorithms (DDA/RecBF,
ReRecBF and Genetic Algorithm) and dashed ones represent sets (dataset, fuzzy rules set and
fuzzy variables set).
The
DDA/RecBF
(Dynamic Decay Adjustment for Rectangular Basis Functions)
algorithm 13 allows to obtain a RecBF Network from a dataset and a definition of the
clusters (classes) of the output variable in a set of fuzzy membership functions.
RecBF Networks 13 are a variation of RBF networks, in which the representation is a
set of hyper-rectangles belonging to the different classes of the system. Every dimen-
sion of the hyper-rectangles represents a membership function. Finally, a network is
built, representing, on every neuron, the membership function found. The algorithm
which produces the RecBFN from the dataset and from the definition of the classes of
the system is called DDA/RecBF. The set of membership functions defined by this
method are usually well suited for classification.
These membership functions will be used to obtain a set of rules by means of a
Genetic Algorithm. Although first, a previous step to transform the set of membership
functions (output of the DDA/RecBF) has to be done since they need to be adapted
for working with imbalanced data. This task is done through the
ReRecBF
algorithm
by recombining the set of membership functions.
Genetic Algorithms 14 are used to derive fuzzy rules from the set of recombined
membership functions. Genetic algorithms are methods based on principles of natural
selection and evolution for global searches. Given a problem, a genetic algorithm runs
repeatedly by using the three fundamental operators: reproduction, crossover and
mutation. These operators, combined randomly, are based on a fitness function evolu-
tion to find a better solution in the searching space. Chromosomes represent the indi-
viduals of the genetic algorithms and a chromosome is composed of several genes.
Genetic algorithms are used to find solutions to problems with a large set of possible
solutions and they have the advantage of only requiring information concerning the
quality of the solution. This fact makes genetic algorithms a very good method to
solve complex problems.
Empirical results show that for the Down's syndrome problem the accuracy is
improved with respect to the current method used. Furthermore, this method has been
compared with other methods for imbalanced problems, using some UCI datasets.
The results show that our method improves the accuracy in most of cases.
