Training Artificial Neural Networks for Fuzzy Logic

P roblems requiring inferencing with Boolean logic have been implemented in percept rons or feedforward networks, and some attempts have been made to implement fuzzy logic based inferencing in similar networks. In this pap er, we present producti ve networks , which are art ificial neur al networks, meant for fuzzy logic based inferencing. The nod es in t hese networks collect an offset product of the inputs, further offset by a bias. A meaning can be assigned to each node in such a network , since the offsets must be eit her -1 , 0, or l. Earlier , it was shown that fuzzy logic inferencing could be performed in productive networks by manu ally setting t he offsets. Thi s procedure, however , encountered crit icism, since t here is a feeling t hat neural networks should involve tr aining. We describe an algorit hm for training pro duct ive networks from a set of training inst ances. Unlike feedforward neur al networks with sigmoida l neurons , these networks can be tra ined wit h a small number of t ra ining instances. T he three main logical operations that form the basis of inferencingNOT, OR , and AND-can be implemented easily in productive networks. T he network s derive their nam e from t he way the offset product of inpu ts forms the act ivation of a node.