Multiple-Valued Logic and Complex-Valued Neural Networks

Abstract

In classical multiple-valued logic its values are encoded by integers. This complicates the use of multiple-valued logic as a basic model, which can be utilized in an artificial neuron, because the values of k-valued logic encoded by integers 0, 1, 2, ..., k are not normalized. To overcome this obstacle, it was suggested to encode the values of k-valued logic by complex numbers located on the unit circle, namely by the kth roots of unity. It is described in the paper how this model of multiple-valued logic over the field of complex numbers was suggested and how it was used to develop a multi-valued neuron (MVN). Then it is considered how a feedforward neural network based on MVN—a multilayer neural network with multi-valued neurons (MLMVN) was designed and its derivative-free learning algorithm based on the error-correction learning rule was presented. Different applications of MLMVN, which outperforms many other machine learning tools in terms of learning speed and generalization capability are also observed.