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Multiple-Valued Threshold Logic and Multi-Valued Neurons

  • Igor N. Aizenberg
  • Naum N. Aizenberg
  • Joos Vandewalle
Chapter

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.

Keywords

Weighting Vector Threshold Function Threshold Logic Structural Alphabet Power Root 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 2000

Authors and Affiliations

  • Igor N. Aizenberg
    • 1
  • Naum N. Aizenberg
    • 1
  • Joos Vandewalle
    • 2
  1. 1.Neural Networks Technologies Ltd.Israel
  2. 2.Departement Elektrotechniek, ESAT/SISTAKatholieke Universiteit LeuvenBelgium

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