Generation of Fuzzy Rules from Decision Trees

Abstract

The paper introduces two ways to develop fuzzy rules, using decision trees, from data with continuous valued inputs and outputs. A key problem is dealing with continuous outputs. Output classes are created, then a crisp decision tree is created using a set of fuzzy output classes and letting each training example to partially belong to classes. Alternatively, a discrete set of fuzzy outputs classes is created that includes a selected group of overlaps, such as class A.75/class B.25. Training examples are then provided to a standard decision tree learning program, such as C4.5. In both cases, fuzzy rules are extracted from the resulting decision tree. Output classes must be created for a case in which examples belong to discrete but overlapping classes. We discuss tradeoffs of the two approaches to output class creation. An example of system performance uses a discrete set of overlapping classes on the Box-Jenkins gas furnace prediction problem and a function approximation problem. The learned rules provide effective control and function approximation.