The Multi-Valued Neuron

Abstract

In this chapter, we introduce the multi-valued neuron. First of all, in Section 2.1 we consider the essentials of the theory of multiple-valued logic over the field of complex numbers. Then we define a threshold function of multiple-valued logic. In Section 2.2, we define the discrete-valued multi-valued neuron whose input/output mapping is always described by some threshold function of multiple-valued logic. Then we consider the continuous multi-valued neuron. In Section 2.3, we consider the edged separation of an n-dimensional space, which is determined by the activation function of the discrete multi-valued neuron, and which makes it possible to solve multi-class classification problems. In Section 2.4, we consider how the multi-valued neuron can be used for simulation of a biological neuron. Some concluding remarks are given in Section 2.5.