On constructing a fuzzy inference framework using crisp decision trees

This paper proposes a framework which consists of a novel fuzzy inference algorithm to generate fuzzy decision trees from induced crisp decision trees. Fuzzy theoretical techniques are used to fuzzify crisp decision trees in order to soften sharp decision boundaries at decision nodes inherent in this type of trees. A framework for the investigation of various types of membership functions and fuzzy inference techniques is proposed. Once the decision tree has been fuzzified, all branches throughout the tree will fire, resulting in a membership grade being generated at each branch. Five different fuzzy inference mechanisms are used to investigate the degree of interaction between membership grades on each path in the decision tree, which ultimately leads to a final crisp classification. A genetic algorithm is used to optimize and automatically determine the set of fuzzy regions for all branches and simultaneously the degree in which the inference parameters will be applied. Comparisons between crisp trees and the fuzzified trees suggest that the later fuzzy tree is significantly more robust and produces a more balanced classification. In addition, the results obtained from five real-world data sets show that there is a significant improvement in the accuracy of the fuzzy trees when compared with crisp trees.