 
Summary: Learning of the NonThreshold Functions of
MultipleValued Logic by a Single MultiValued
Neuron With a Periodic Activation Function
Igor Aizenberg
Department of Computer Science
Texas A&M UniversityTexarkana
Texarkana, USA
igor.aizenberg@tamut.edu
Abstract In this paper, a theory of multiplevalued threshold
functions over the field of complex numbers is further developed.
kvalued threshold functions over the field of complex numbers
can be learned using a single multivalued neuron (MVN). We
propose a new approach for the projection of a kvalued function,
which is not a threshold one, to mvalued logic (m>k), where this
function becomes a partially defined mvalued 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 multiplevalued functions
using a single MVN.
