This paper introduces a new approach to enhance performance in performing logic programming in the Hopfield neural network by using agent-based modeling. Hopfield networks have been broadly utilized to solve problems of combinatorial optimization. However, this network yielded a satisfiability problem because the network has grown larger, and it is more complex. Therefore, an improved algorithm has been proposed to enhance the Hopfield network’s capability by using the technique of fuzzy logic to provide more efficient energy relaxation and to avoid the local minimum solutions. Agent-based modeling has been introduced in this paper to conduct computer simulations, which aim at verifying and validating the introduced approach. By applying the technique of fuzzy Hopfield neural network clustering in the system, better quality solutions are produced, and the network is handled better despite the increasing complexity. Also, the solutions converged faster by the system. Accordingly, this technique of the fuzzy Hopfield neural network clustering in the system has produced better-quality solutions.

The artificial neural network system's dynamical behaviors are greatly dependent on the construction of the network. Artificial Neural Network's outputs suffered from a shortage of interpretability and variation lead to severely limited the practical usability of artificial neural networks for doing the logical program. The goal for implementing a logical program in Hopfield neural network rotates rounding minimizing the energy function of the network to reaching the best global solution which ordinarily fetches local minimum solution also. Nevertheless, this problem can be overcome by utilizing the hyperbolic tangent activation function and the Boltzmann Machine in the Hopfield neural network. The foremost purpose of this article is to explore the solution quality obtained from the Hopfield neural network to solve 2 Satisfiability logic (2SAT) by using the Mean-Field Theory algorithm. We want for replacing the real unstable prompt local field for the separate neurons into the network by its average local field utility. By using the solution to the deterministic Mean-Field Theory (MFT) equation, the system will derive the training algorithms in which time-consuming stochastic measures of collections are rearranged. By evaluating the outputs of global minima ratio (zM), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE) with computer processing unit (CPU) time as benchmarks, we find that the MFT theory successfully captures the best global solutions by relaxation effects energy function.