Rule set reduction in fuzzy decision trees

The ID3 algorithm forms the basis for many decision trees´ algorithms and programs. Trees produced by this algorithm are known to be very sensitive to small changes in attribute values. Fuzzy ID3 is an extension of ID3; it integrates fuzzy set theory and fuzzy logic with ID3. This integration reduces the sensitivity of the produced decision trees to small changes in attribute values, and helps in overcoming the effects of spurious precision in the data. In a previous work, we presented a modified version of the fuzzy ID3 algorithm that integrates information gain and classification ambiguity to select the split attribute and showed that the modified version can achieve better accuracy on a wide range of datasets. However the number of generated fuzzy rules was very high. In this paper, we introduce a new threshold value on the membership value of an object to propagate from a parent node to child nodes in the fuzzy decision tree. In addition we introduce a new syntax for fuzzy rules; the new syntax utilizes partial membership ratios of different classes in a leaf node. The modified version achieved a significant reduction in the number of generated fuzzy rules, and results in a huge decrease in run-time and better accuracy.