The Generation of Fuzzy Rules from Decision Trees

This paper introduces two methods of developing fuzzy rules, using decision trees, from data with continuous valued inputs and outputs. A key problem is how to deal with continuous outputs. Here output classes are created. A crisp decision tree may then be created using a set of fuzzy output classes allowing each training example to partially belong to the classes. Alternatively, a discrete set of fuzzy outputs classes can be created which include a selected group of overlaps, such as classA.75/classB.25. The training examples can then be provided to a standard decision tree learning program, such as C4.5. In both cases fuzzy rules will be extracted from the resultant decision tree. Output classes will have to be created for the case in which examples belong to discrete, but overlapping multiple classes. We discuss the tradeoffs of the two approaches to output class creation. An example of the systems performance using a discrete set of overlapping classes on the the Box-Jenkins gas furnace prediction problem and a function approximation problem are given. The learned rules are able to provide effective control and function approximation.