Extraction of fuzzy logic rules from data by means of artificial neural networks

The extraction of logical rules from data has been, for nearly fifteen years, a key application of artificial neural networks in data mining. Although Boolean rules have been extracted in the majority of cases, also methods for the extraction of fuzzy logic rules have been studied increasingly often. In the paper, those methods are discussed within a five-dimensional classification scheme for neural-networks based rule extraction, and it is pointed out that all of them share the feature of being based on some specialized neural network, constructed directly for the rule extraction task. As an important representative, a method for the extraction of rules in a general fuzzy disjunctive normal form is described in detail and illustrated on real-world applications. Finally, the paper proposes an algorithm demonstrating a principal possibility to extract fuzzy logic rules from multilayer perceptrons with continuous activation functions, i.e., from the kind of neural networks most universally used in applications. However, complexity analysis of the individual steps of that algorithm reveals that it involves computations with doubly-exponential complexity, due to which it can not without simplifications serve as a practically applicable alternative to methods based on specialized neural networks.