One of the main problems in representing information in the form of nonsystematic logic is the lack of flexibility, which leads to potential overfitting. Although nonsystematic logic improves the representation of the conventional k Satisfiability, the formulations of the first, second, and third-order logical structures are very predictable. This paper proposed a novel higher-order logical structure, named G-Type Random k Satisfiability, by capitalizing the new random feature of the first, second, and third-order clauses. The proposed logic was implemented into the Discrete Hopfield Neural Network as a symbolic logical rule. The proposed logic in Discrete Hopfield Neural Networks was evaluated using different parameter settings, such as different orders of clauses, different proportions between positive and negative literals, relaxation, and differing numbers of learning trials. Each evaluation utilized various performance metrics, such as learning error, testing error, weight error, energy analysis, and similarity analysis. In addition, the flexibility of the proposed logic was compared with current state-of-the-art logic rules. Based on the simulation, the proposed logic was reported to be more flexible, and produced higher solution diversity.

The primary objective of introducing metaheuristic algorithms into traditional systematic logic is to minimize the cost function. However, there is a lack of research on the impact of introducing metaheuristic algorithms on the cost function under different proportions of positive literals. In order to fill in this gap and improve the efficiency of the metaheuristic algorithm in systematic logic, we proposed a metaheuristic algorithm based on mutation tabu search and embedded it in probabilistic satisfiability logic in discrete Hopfield neural networks. Based on the traditional tabu search algorithm, the mutation operators of the genetic algorithm were combined to improve its global search ability during the learning phase and ensure that the cost function of the systematic logic converged to zero at different proportions of positive literals. Additionally, further optimization was carried out in the retrieval phase to enhance the diversity of solutions. Compared with nine other metaheuristic algorithms and exhaustive search algorithms, the proposed algorithm was superior to other algorithms in terms of time complexity and global convergence, and showed higher efficiency in the search solutions at the binary search space, consolidated the efficiency of systematic logic in the learning phase, and significantly improved the diversity of the global solution in the retrieval phase of systematic logic.

In the realm of activity recognition, the Fuzzy K-Nearest Neighbors (FKNN) algorithm stands as a pivotal technique for classification tasks. However, the performance of FKNN is heavily reliant on the choice of its hyperparameters, notably the number of neighbors (k) and the fuzziness parameter (m). Optimizing these hyperparameters is a non-trivial challenge, significantly affecting classification accuracy. To address this challenge, an integrated approach that combines Principal Component Analysis (PCA) and an adaptive grid search algorithm for hyperparameter tuning is proposed. Utilizing a dataset captured from a Wireless Sensor Network (WSN) that measures Received Signal Strength (RSS) from sensor nodes placed on a user’s chest and ankles, the methodology initiates with preprocessing to extract time-domain features, such as mean and variance, from the raw RSS data. Strategic ranges for hyperparameters are defined to effectively explore the parameter space. PCA is employed to reduce dimensionality and enhance data structure visibility. The core of the approach lies in adaptive grid search, which iteratively refines the hyperparameter search space based on observed performance metrics, converging on optimal values that yield the highest classification accuracy. The FKNN model, trained with these optimized parameters, is then evaluated on a separate test set. Results demonstrate that this approach not only enhances the classification accuracy of the FKNN algorithm but also achieves a balanced performance in activity recognition using multisensor data fusion.

The Sparrow search algorithm is a new and effective swarm intelligence method proposed in recent years and studied in many publications. Based on the basic principle of sparrow search algorithm, this paper combines the inverse learning algorithm with the refined inverse solution to form an improved sparrow search (SSA) algorithm. Combining the fuzzy k-nearest neighbor method and the improved SSA, the numerical simulation of two-classes datasets and multi-classes datasets is carried out, and many numerical results are obtained, and the results are analyzed. At the same time, this paper lists the data comparison results and tables with other models. The hybrid SSA-FKNN proposed in this paper has a clear advantage in terms of accuracy (ACC).

The efficiency of learning algorithm can be improved by introducing propositional satisfiability in Discrete Hopfield Neural Network and modeling the neuron str