Randomised Alpha-Cut Fuzzy Logic Hybrid Model in Solving 3-Satisfiability Hopfield Neural Network


  • Farah Liyana Azizan ᵃSchool of Mathematical Sciences, Universiti Sains Malaysia, Penang, 11800, USM, Malaysia; ᵇCentre for Pre-University Studies, Universiti Malaysia Sarawak, 94300, Kota Samarahan, Sarawak, Malaysia https://orcid.org/0000-0002-8070-8206
  • Saratha Sathasivam School of Mathematical Sciences, Universiti Sains Malaysia, Penang, 11800, USM, Malaysia https://orcid.org/0000-0002-2843-7082




3-Satisfiability, Alpha-cut, Fuzzy logic, Hopfield Network, Logic programming


This paper proposes an innovative approach to improve the performance of 3SAT logic programming in the Hopfield neural network. The merged structures of the 3SAT and Hopfield network have specific weaknesses, one of which is that, at times, the system attained local minimum solutions rather than global minimum solutions. A new model of integration randomised alpha-cut fuzzy logic with 3SAT in the Hopfield network is built to convey information more effectively. 3SAT and fuzzy logic can work together to solve Hopfield networks' combinatorial optimisation issues. Procedures of fuzzifying and defuzzifying the neurons might ease the computational burden of determining the correct neuron states. Until the proper neuron state is established, unsatisfied neuron clauses will be modified using a randomised alpha-cut approach in the defuzzifier step. An incorporated design built a random approach to select the alpha-cut values of 0.1, 0.25, and 0.5. At this point, a fuzzy value switches into a crisp output back through the defuzzifier process. Based on the results obtained, the proposed hybrid strategy effectively improves the indicators of RMSE, SSE, MAE, MAPE, global minima and total computational time. A computer-generated data set was used to measure how well the hybridised techniques performed. The performance of the proposed network was trained and validated using Matlab 2020b. The results are significant because this model significantly affects how successfully Hopfield networks merged with fuzzy logic can tackle the 3SAT challenges. The obtained data and ideas will help to create novel approaches to data collection for upcoming logic programming exploration.


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