Rule extraction with fuzzy neural network

This paper deals with the learning of understandable decision rules with connectionist systems. Our approach consists of extracting fuzzy control rules with a new fuzzy neural network. Whereas many other works on this area propose to use combinations of nonlinear neurons to approximate fuzzy operations, we use a fuzzy neuron that computes max-min operations. Thus, this neuron can be interpreted as a possibility estimator, just as sigma-pi neurons can support a probabilistic interpretation. Within this context, possibilistic inferences can be drawn through the multi-layered network, using a distributed representation of the information. A new learning procedure has been developed in order that each part of the network can be learnt sequentially, while other parts are frozen. Each step of the procedure is based on the same kind of learning scheme: the backpropagation of a well-chosen cost function with appropriate derivatives of max-min function. An appealing result of the learning phase is the ability of the network to automatically reduce the number of the condition-parts of the rules, if needed. The network has been successfully tested on the learning of a control rule base for an inverted pendulum.