Genetic Fuzzy Discretization for Classification Problems

Many real-world classification algorithms can not be applied unless the continuous attributes are discretized and the interval discretization methods are used in many machine learning techniques. It is hard to determine the intervals for the discretization of numerical attributes that has an infinite number of candidates. And interval discretization methods are based on a crisp set, a value in a continuous attribute must belong to only one interval. They are often not proper for describing a value located around the boundaries of intervals. Fuzzy partioning is an attractive method for those cases in classification problems. An important decision in fuzzy partitioning is about the positions of interval boundaries and the degrees of overlapping in the fuzzy sets. We optimize the parameters that specify fuzzy partitioning by genetic algorithms. We divide the range of a continuous attribute into k intervals and represent each value by a k-bit string where each bit corresponds to one interval. The i bit of the binary string represents whether the value belongs to the i interval or not. While a value belongs to only one interval in a simple discretization, it can belong to more than one interval in fuzzy discretization. Thus a value can be represented by a binary mask. For example, in Fig. 1, the value 0.595 belongs to the third and fourth intervals and is represented by a binary mask 00110. It provides more flexibility in machine learning algorithms for pattern classification. We optimize the boundaries of intervals and the degrees of overlapping in fuzzy discretization. We use four parameters for each interval Ii: ti, ti+1, li and ui. The genetic fuzzy membership function is defined as follows: