Learning of the Non-threshold Functions of Multiple-Valued Logic by a Single Multi-valued Neuron with a Periodic Activation Function

In this paper, a theory of multiple-valued threshold functions over the field of complex numbers is further developed. k-valued threshold functions over the field of complex numbers can be learned using a single multi-valued neuron (MVN). We propose a new approach for the projection of a k-valued function, which is not a threshold one, to m-valued logic (m≫k), where this function becomes a partially defined m-valued threshold function and can be learned by a single MVN. To build this projection, a periodic activation function for the MVN is used. This new activation function and a modified learning algorithm make it possible to learn nonlinearly separable multiple-valued functions using a single MVN.