On the Use of Fuzzy Trees for Solving Classification Problems with Numeric Outcomes

This paper introduces a novel algorithm which applies the theories of fuzzification in order to fuzzify decision trees for solving classification problems with numeric outcomes. The CHAID algorithm is a highly efficient statistical technique for segmentation, or tree growing. The application of fuzzy logic to pre-generated CHAID decision trees can represent classification knowledge more naturally and in-line with human thinking. Using a genetic algorithm (GA), various sized fuzzy regions are optimised from a training set and are applied to all decision nodes within the tree. A new case passing through the tree results in a membership grade being generated at each branch. Four different fuzzy inference mechanisms, also optimised by the GA, are used to investigate the degree of interaction between membership grades on each specific decision path. A modified approach to Mamdani´s inference is also proposed to manage the defuzzification of numeric tree outcomes. Initial comparisons between crisp and fuzzified CHAID trees show that the fuzzy tree is more robust and produces a more balanced classification leading to improved decision making