Existing deep learning real denoising methods require a large amount of noisyclean image pairs for supervision. Nonetheless, capturing a real noisy-clean dataset is an unacceptable expensive and cumbersome procedure. To alleviate this problem, this work investigates how to generate realistic noisy images. Firstly, we formulate a simple yet reasonable noise model that treats each real noisy pixel as a random variable. This model splits the noisy image generation problem into two subproblems: image domain alignment and noise domain alignment.

Information Filtering Networks (IFNs) provide a powerful framework for modeling complex systems through globally sparse yet locally dense and interpretable structures that capture multivariate dependencies. This review offers a comprehensive account of IFNs, covering their theoretical foundations, construction methodologies, and diverse applications. Tracing their origins from early network-based models to advanced formulations such as the Triangulated Maximally Filtered Graph (TMFG) and the Maximally Filtered Clique Forest (MFCF), the paper highlights how IFNs address key challenges in high-dimensional data-driven modeling. IFNs and their construction methodologies are intrinsically higher-order networks that generate simplicial complexes-structures that are only now becoming popular in the broader literature. Applications span fields including finance, biology, psychology, and artificial intelligence, where IFNs improve interpretability, computational efficiency, and predictive performance. Special attention is given to their role in graphical modeling, where IFNs enable the estimation of sparse inverse covariance matrices with greater accuracy and scalability than traditional approaches like Graphical LASSO. Finally, the review discusses recent developments that integrate IFNs with machine learning and deep learning, underscoring their potential not only to bridge classical network theory with contemporary data-driven paradigms, but also to shape the architectures of deep learning models themselves.

Modern applications of artificial intelligence in decision support systems, plan generation systems require reasoning with imprecise a nd uncertain information. Logical frameworks based on bivalent reasoning are not suitable for such applications, because the set {0, 1} cannot capture the vagueness or uncertainty of underlying proposition. Though fuzzy log ic-based systems can represent imprecise linguistic information by ascribi ng membership values to attributes (or truth values to propositions) taken fr om the interval 1 [0,1], but this graded valuation becomes inadequate if the p recise membership can not be determined due to some underlying uncerta inty. This uncertainty may arise from lack of complete information or f rom lack of reliability of source of information or lack of unanimity amon g rational agents in a multi-agent reasoning system or from many other reasons . This uncertainty with respect to the assignment of membership degr ees is captured by assigning a range of possible membership values, i.e. by a ssigning an interval.