An initial comparison of generalization-capability between crisp and fuzzy decision trees

Crisp decision trees are based on the precondition that linguistic terms and classes are crisp whereas fuzzy decision trees, which are an extension of the crisp case, are based on fuzzy valued attributes and classes. Fuzzy decision tree is popular in dealing with the ambiguity and vagueness associated with human thinking. The generalization capability of decision tree, which is also called the predictive capability, is one of the most important indexes to judge whether a decision tree generation algorithm is good. The stronger the generalization is, the higher the prediction accuracy. In practical applications, the generalization capability of a decision tree algorithm directly affects the accuracy of decision-making. However, so far nobody has given a comparison study between the generalization capabilities of fuzzy and crisp decision tree algorithms. This paper attempts to compare the generalization capability of fuzzy and crisp decision trees in three aspects. It aims to provide some useful guidelines for selecting either a crisp or a fuzzy algorithm while decision tree induction is applicable to real problems.