Fuzzy modeling with decision trees

Decision trees are a well-known and widely used method for classification problems. For handling numerical attributes or even for numerical prediction, traditional decision trees based on crisp predicates are not suitable. Through the usage of fuzzy predicates for different types of attributes, not only the expressive power of decision trees can be extended, but it also allows to create models for numerical attributes in a very natural manner. We present a logical foundation for inductive learning of fuzzy decision trees. We further show how fuzzy logical inference methods can be applied with fuzzy decision trees to provide continuous output. Extending the underlying logical language with ordering-based fuzzy predicates enables as to generate not only more compact, but also more accurate, decision trees. These explanations are complemented by remarks on how the obtained results can be interpreted and altered by the user, to provide a theoretically founded method for interactive data analysis.