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.
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© 2000 Springer Science+Business Media Dordrecht
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Aizenberg, I.N., Aizenberg, N.N., Vandewalle, J. (2000). Multiple-Valued Threshold Logic and Multi-Valued Neurons. In: Multi-Valued and Universal Binary Neurons. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-3115-6_2
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DOI: https://doi.org/10.1007/978-1-4757-3115-6_2
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4978-3
Online ISBN: 978-1-4757-3115-6
eBook Packages: Springer Book Archive