Adjusting fuzzy partitions by genetic algorithms and histograms for pattern classification problems

For function approximation using fuzzy if-then rules, Nomura et al. (1992) proposed a genetic algorithm-based method for adjusting the fuzzy partition of an input space. In this paper, we apply their method to pattern classification problems. We have already extended the coding method in their work to the case where intervals and trapezoidal membership functions can be used for antecedent fuzzy sets. There are, however, two drawbacks in these methods. One is that the resolution of each axis on which the fuzzy partition was adjusted should be prespecified by a decision-maker for genetic algorithms. The other is that the number of fuzzy if-then rules generated by these coding methods exponentially increases as the number of attributes increases. To cope with the first drawback, we propose a coding method using histograms where a distribution of training patterns is considered to specify the resolution of each axis. For the second drawback, we employ an input selection procedure. Using this procedure, our genetic-algorithm-based fuzzy partition method can be applied to high-dimensional pattern classification problems.