In classical multiple-valued logic its values are encoded by integers. This complicates the use of multiple-valued logic as a basic model, which can be utilized in an artificial neuron, because the values of k-valued logic encoded by integers 0, 1, 2, …, k are not normalized. To overcome this obstacle, it was suggested to encode the values of k-valued logic by complex numbers located on the unit circle, namely by the kth roots of unity. It is described in the paper how this model of multiple-valued logic over the field of complex numbers was suggested and how it was used to develop a multi-valued neuron (MVN). Then it is considered how a feedforward neural network based on MVN-a multilayer neural network with multi-valued neurons (MLMVN) was designed and its derivative-free learning algorithm based on the error-correction learning rule was presented. Different applications of MLMVN, which outperforms many other machine learning tools in terms of learning speed and generalization capability are also observed.
CITATION STYLE
Aizenberg, I. (2017). Multiple-valued logic and complex-valued neural networks. In Studies in Fuzziness and Soft Computing (Vol. 349, pp. 153–171). Springer Verlag. https://doi.org/10.1007/978-3-319-48317-7_10
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