MULTIPLE-VALUED NEURO-ALGEBRA

A new arithmetic multiple-valued algebra with functional completeness is introduced. The algebra is called Neuro-Algebra for it has very sim ilar formula and architecture to neural networks. Two canonical forms of multiple-valued functions of this Neuro-Algebra are presented. Sinc e the arithmetic operations of the Neuro-Algebra are basically a weigh ted-sum and a piecewise linear operations, their implementations are v ery simple and straightforward. Furthermore, the multiple-valued netwo rks based on the Neuro-Algebra can be trained by the traditional back- propagation learning algorithm directly.