Training Artificial Neural Networks for Fuzzy Logic
Abhay Bulsari
On leave from Lappeenranta University of Technology.
Kemisk-tekniska fakulteten, Abo Akademi,
SF 20500 Turku/Abo, Finland
Abstract
Problems requiring inferencing with Boolean logic have been implemented in perceptrons or feedforward networks, and some attempts have been made to implement fuzzy logic based inferencing in similar networks. In this paper, we present productive networks, which are artificial neural networks, meant for fuzzy logic based inferencing. The nodes in these 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 either -1, 0, or 1.
Earlier, it was shown that fuzzy logic inferencing could be performed in productive networks by manually setting the offsets. This procedure, however, encountered criticism, since there is a feeling that neural networks should involve training. We describe an algorithm for training productive networks from a set of training instances. Unlike feedforward neural networks with sigmoidal neurons, these networks can be trained with a small number of training instances.
The three main logical operations that form the basis of inferencing---NOT, OR, and AND---can be implemented easily in productive networks. The networks derive their name from the way the offset product of inputs forms the activation of a node.
