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Random Maximum 2 Satisfiability Logic in Discrete Hopfield Neural Network Incorporating Improved Election Algorithm

Author

Listed:
  • Vikneswari Someetheram

    (School of Mathematical Sciences, Universiti Sains Malaysia—USM, Gelugor 11800, Penang, Malaysia)

  • Muhammad Fadhil Marsani

    (School of Mathematical Sciences, Universiti Sains Malaysia—USM, Gelugor 11800, Penang, Malaysia)

  • Mohd Shareduwan Mohd Kasihmuddin

    (School of Mathematical Sciences, Universiti Sains Malaysia—USM, Gelugor 11800, Penang, Malaysia)

  • Nur Ezlin Zamri

    (School of Distance Education, Universiti Sains Malaysia—USM, Gelugor 11800, Penang, Malaysia)

  • Siti Syatirah Muhammad Sidik

    (School of Mathematical Sciences, Universiti Sains Malaysia—USM, Gelugor 11800, Penang, Malaysia)

  • Siti Zulaikha Mohd Jamaludin

    (School of Mathematical Sciences, Universiti Sains Malaysia—USM, Gelugor 11800, Penang, Malaysia)

  • Mohd. Asyraf Mansor

    (School of Distance Education, Universiti Sains Malaysia—USM, Gelugor 11800, Penang, Malaysia)

Abstract

Real life logical rule is not always satisfiable in nature due to the redundant variable that represents the logical formulation. Thus, the intelligence system must be optimally governed to ensure the system can behave according to non-satisfiable structure that finds practical applications particularly in knowledge discovery tasks. In this paper, we a propose non-satisfiability logical rule that combines two sub-logical rules, namely Maximum 2 Satisfiability and Random 2 Satisfiability, that play a vital role in creating explainable artificial intelligence. Interestingly, the combination will result in the negative logical outcome where the cost function of the proposed logic is always more than zero. The proposed logical rule is implemented into Discrete Hopfield Neural Network by computing the cost function associated with each variable in Random 2 Satisfiability. Since the proposed logical rule is difficult to be optimized during training phase of DHNN, Election Algorithm is implemented to find consistent interpretation that minimizes the cost function of the proposed logical rule. Election Algorithm has become the most popular optimization metaheuristic technique for resolving constraint optimization problems. The fundamental concepts of Election Algorithm are taken from socio-political phenomena which use new and efficient processes to produce the best outcome. The behavior of Random Maximum 2 Satisfiability in Discrete Hopfield Neural Network is investigated based on several performance metrics. The performance is compared between existing conventional methods with Genetic Algorithm and Election Algorithm. The results demonstrate that the proposed Random Maximum 2 Satisfiability can become the symbolic instruction in Discrete Hopfield Neural Network where Election Algorithm has performed as an effective training process of Discrete Hopfield Neural Network compared to Genetic Algorithm and Exhaustive Search.

Suggested Citation

  • Vikneswari Someetheram & Muhammad Fadhil Marsani & Mohd Shareduwan Mohd Kasihmuddin & Nur Ezlin Zamri & Siti Syatirah Muhammad Sidik & Siti Zulaikha Mohd Jamaludin & Mohd. Asyraf Mansor, 2022. "Random Maximum 2 Satisfiability Logic in Discrete Hopfield Neural Network Incorporating Improved Election Algorithm," Mathematics, MDPI, vol. 10(24), pages 1-29, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4734-:d:1002100
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    References listed on IDEAS

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