Aiming at the problem that the global search performance of a transiently chaotic neural network is not ideal, a multiple frequency conversion sinusoidal chaotic neural network (MFCSCNN) model is proposed based on the biological mechanism of the brain, including multiple functional modules and sinusoidal signals of different frequencies. In this model, multiple FCS functions and Sigmoid functions with different phase angles were used to construct the excitation function of neurons in the form of weighted sum. In this paper, the inverted bifurcation diagram, Lyapunov exponential diagram and parameter range of the model are given. The dynamic characteristics of the model are analyzed and applied to function optimization and combinatorial optimization problems. Experimental results show that the multiple frequency conversion sinusoidal chaotic neural network has better global search performance than the transient chaotic neural network and other related models.

Restricted Boltzmann Machines (RBMs) struggle with real-world data noise due to deterministic parameters. While fuzzy RBMs (FRBMs) introduce uncertainty modeling, Type-1 FRBMs suffer from information loss during defuzzification. To address these limitations, this paper proposes an Interval Type-2 Fuzzy RBM (IT2FRBM) framework based on crisp possibilistic mean defuzzification. First, leveraging interval type-2 fuzzy theory, we construct three types of fuzzy parameters—Symmetric/Asymmetric Triangular Fuzzy Numbers (STFN/ATFN) and Gaussian Fuzzy Numbers (GFN)—to enhance the model’s expressive capability for complex data. Second, we extend the crisp possibilistic mean defuzzification method to interval type-2 fuzzy sets. Compared to traditional $\alpha $ -cut-based defuzzification, this extension enables a more straightforward derivation of the defuzzified free energy function. Furthermore, we derive error approximation bounds for different fuzzy numbers, which both demonstrate the rationality of the approximation and simplify computation. Experimental results on image reconstruction tasks show that the three proposed IT2FRBM variants achieve significant improvements in both reconstruction quality and robustness compared to classical RBM, FRBM variants, and other baseline methods, demonstrating their potential for robust feature extraction and image denoising in noisy environments. Note to Practitioners—In practical industrial scenarios such as quality inspection and sensor monitoring, data are often contaminated by noise, ambiguity, or incompleteness. Traditional deep learning models, e.g., the Restricted Boltzmann Machine (RBM), possess fixed parameters and thus exhibit limited adaptability to such uncertainties, resulting in insufficient robustness and performance. To address this issue, this paper proposes an Interval Type-2 Fuzzy Restricted Boltzmann Machine (IT2FRBM), which extends model parameters into interval type-2 fuzzy sets. This design allows connection weights to dynamically adjust their value ranges and distribution shapes according to the uncertainty present in the input data, thereby natively absorbing noise and fuzziness within the model and significantly improving its adaptability to dynamically changing data. The proposed method demonstrates clear advantages in noise robustness, feature learning quality, and training efficiency: it achieves lower image reconstruction error under noisy conditions, produces reconstructed images with higher clarity and structural fidelity on benchmark datasets, and more than doubles the training speed compared to existing interval type-2 fuzzy RBM variants, making it more suitable for practical deployment. The framework can be directly applied to tasks such as image denoising, enhancement, and feature extraction from noisy data. The main limitations of the current approach lie in its relatively high computational cost and its relatively simple structure. Future work may focus on extending the framework to continuous data or deeper network architectures, as well as designing more lightweight training algorithms, thereby broadening its applicability in the fields of industrial sensing and visual inspection.