The Method of Construction of Logical Neural Networks on the Basis of Variable-Valued Logical Functions

Abstract

In this paper, we suggest a method of constructing logical neural networks on the basis of variable-valued logical functions. We prove the theorem on a possibility of representation of any logical function as a logical neural network. The proof given in the paper contains an algorithm of the construction of the logical neural network. We point out the possibility of the generalization of the result obtained to the case of fuzzy logic.

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Correspondence to D. P. Dmitrichenko.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 154, Proceedings of the International Conference “Actual Problems of Applied Mathematics and Physics,” Kabardino-Balkaria, Nalchik, May 17–21, 2017, 2018.

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Dmitrichenko, D.P., Zhilov, R.A. The Method of Construction of Logical Neural Networks on the Basis of Variable-Valued Logical Functions. J Math Sci 253, 500–505 (2021). https://doi.org/10.1007/s10958-021-05246-0

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Keywords and phrases

  • variable-valued predicate
  • data mining
  • variable-valued logical function
  • training sample
  • logical neural network
  • fuzzy logic

AMS Subject Classification

  • 68T27