Selecting Correct Methods to Extract Fuzzy Rules from Artificial Neural Network

Abstract

Artificial neural network (ANN) inherently cannot explain in a comprehensible form how a given decision or output is generated, which limits its extensive use. Fuzzy rules are an intuitive and reasonable representation to be used for explanation, model checking, and system integration. However, different methods may extract different rules from the same ANN. Which one can deliver good quality such that the ANN can be accurately described by the extracted fuzzy rules? In this paper, we perform an empirical study on three different rule extraction methods. The first method extracts fuzzy rules from a fuzzy neural network, while the second and third ones are originally designed to extract crisp rules, which can be transformed into fuzzy rules directly, from a well-trained ANN. In detail, in the second method, the behavior of a neuron is approximated by (continuous) Boolean functions with respect to its direct input neurons, whereas in the third method, the relationship between a neuron and its direct input neurons is described by a decision tree. We evaluate the three methods on discrete, continuous, and hybrid data sets by comparing the rules generated from sample data directly. The results show that the first method cannot generate proper fuzzy rules on the three kinds of data sets, the second one can generate accurate rules on discrete data, while the third one can generate fuzzy rules for all data sets but cannot always guarantee the accuracy, especially for data sets with poor separability. Hence, our work illustrates that, given an ANN, one should carefully select a method, sometimes even needs to design new methods for explanations.