Pattern Trees for Regression and Fuzzy Systems Modeling

Fuzzy pattern tree induction has recently been introduced as a novel classification method in the context of machine learning. Roughly speaking, a pattern tree is a hierarchical, tree-like structure, whose inner nodes are marked with generalized (fuzzy) logical operators and whose leaf nodes are associated with fuzzy predicates on input attributes. In this paper, we adapt the method of pattern tree induction so as to make it applicable to another learning task, namely regression. Thus, instead of predicting one among a finite number of discrete class labels, we address the problem of predicting a real-valued target output. Apart from showing that fuzzy pattern trees are able to approximate real-valued functions in an accurate manner, we argue that such trees are also interesting from a modeling point of view. In fact, by describing a functional relationship between several input attributes and an output variable in an interpretable way, pattern trees constitute a viable alternative to classical fuzzy rule models. Compared to flat rule models, the hierarchical structure of patterns trees further allows for a more compact representation and for trading off accuracy against model simplicity in a seamless manner.