Multiple-Valued Threshold Logic and Multi-Valued Neurons

Abstract

In this Chapter multi-valued neurons are considered. The theoretical background of multi-valued neurons is theory of multiple-valued threshold logic over the field of the complex numbers. It is a deep mathematical generalization of Boolean threshold logic. Section 2.1 is devoted to a general approach for multiple-valued threshold logic, and group’s characters as its main mathematical instrument. Section 2.2 is devoted to multiple-valued threshold functions over the field of the complex numbers and their features. The notion of multi-valued neuron as neural element, which implements input/output mapping described by multiple-valued threshold function is given in Section 2.3. We also present geometrical and topological interpretation of such a mapping. Section 2.4 is devoted to the synthesis of. multi-valued neuron by linear programming method.