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This study, utilizing high-throughput technologies and Machine Learning (ML), has identified gene biomarkers and molecular signatures in Inflammatory Bowel Disease (IBD). We could identify significant upregulated or downregulated genes in IBD patients by comparing gene expression levels in colonic specimens from 172 IBD patients and 22 healthy individuals using the GSE75214 microarray dataset. Our ML techniques and feature selection methods revealed six Differentially Expressed Gene (DEG) biomarkers (VWF, IL1RL1, DENND2B, MMP14, NAAA, and PANK1) with strong diagnostic potential for IBD. The Random Forest (RF) model demonstrated exceptional performance, with accuracy, F1-score, and AUC values exceeding 0.98. Our findings were rigorously validated with independent datasets (GSE36807 and GSE10616), further bolstering their credibility and showing favorable performance metrics (accuracy: 0.841, F1-score: 0.734, AUC: 0.887). Our functional annotation and pathway enrichment analysis provided insights into crucial pathways associated with these dysregulated genes. DENND2B and PANK1 were identified as novel IBD biomarkers, advancing our understanding of the disease. The validation in independent cohorts enhances the reliability of these findings and underscores their potential for early detection and personalized treatment of IBD. Further exploration of these genes is necessary to fully comprehend their roles in IBD pathogenesis and develop improved diagnostic tools and therapies. This study significantly contributes to IBD research with valuable insights, potentially greatly enhancing patient care.

This study proposes novel operational laws that extend the Frank t-norm and t-conorm to develop a new class of aggregation operators (AOs), namely the quasirung orthopair fuzzy Frank weighted average, weighted geometric, ordered weighted average, and ordered weighted geometric operators. These operators are specifically designed to manage uncertain and imprecise information within multi-attribute group decision-making (MGADM) environments. The proposed operators exhibit desirable mathematical properties such as flexibility, robustness, and compatibility, making them highly suitable for complex fuzzy decision contexts. Flexibility is notably enhanced through the independent tuning of the parameters , , and , allowing for more refined control over membership (MD), non-membership (NMD), and interaction behaviors. An entropy-based approach is employed to objectively determine unknown attribute weights, minimizing subjective bias. A real-world case study on the selection of an optimal investment location demonstrates the practical applicability of the proposed method. The results show an improvement in decision-making accuracy by approximately 7.5% compared to traditional approaches. Sensitivity analysis confirms the stability and reliability of the proposed operators under varying conditions. Comparative results further highlight the method’s superiority in terms of accuracy, interpretability, and adaptability to input variations. The paper concludes by outlining special cases and acknowledging certain limitations, offering directions for future research.

This article investigated the solitary wave solutions to the (2+1)-dimensional integrable Schwarz–Korteweg–de Vries equation. The proposed model is particularly applicable to shallow water wave dynamics and may also extend to contexts such as acoustic wave propagation, nonlinear electric media, and oceanic wave phenomena. First, we constructed the ordinary differential equation form of the nonlinear partial differential equation with the help of the traveling wave transformation. After that, we utilized the generalized Arnous method and the modified sub-equation method to construct the solitary waves containing hyperbolic, exponential, trigonometric, and inverse functions. Using suitable parameter values, the graphical aspects of solutions are demonstrated by plotting a 3D surface plot (including a contour and density plot), a 2D surface plot, a streamline plot, and a polar plot. By utilizing these approaches, accurate analytical solutions for soliton waves were generated, which comprise kink, bright, and dark waves. We employed the generalized Arnous method and the modified sub-equation method to formulate a technique for addressing integrable systems, providing a valuable framework for examining nonlinear phenomena across various physical contexts. This study's outcomes enhance both nonlinear dynamical processes and solitary wave theory.

The study of similarity and distance measures plays a key role in understanding the relationships between fuzzy sets and their extensions, especially when applied to decision-making problems. While there has been notable progress in developing similarity measures for various types of generalized fuzzy sets, including fractional fuzzy sets, there is still a lack of well-developed measures suited to the structure of fractional fuzzy sets. This limitation reduces the effectiveness of fuzzy models in complex decision-making tasks where uncertainty needs to be handled more carefully and flexibly. To overcome this issue, we introduce new similarity measures that use three independent fractional exponents , , and corresponding to the membership, neutral, and non-membership degrees. This approach offers greater flexibility and a more detailed way of capturing the relationships between fuzzy values. We also apply these similarity measures within a decision-making model designed to assess alternatives in uncertain environments. The proposed method is tested through a multi-criteria decision-making case study. The results highlight that regulatory and policy barriers ( ​) are the most influential factor, with a final score of , showing the method’s usefulness in real-world settings. Compared to other approaches, our framework adapts better to changes in uncertainty, responds more accurately to variations in input values, and offers clearer, more interpretable results.

The purpose of this work is to investigate the approach to 3-D column graphs in multiplicative generalized metric spaces (MGM-spaces) utilizing single-valued mappings with an application. In MGM-space, we use weakly compatible four self-mappings to prove common fixed point (CFP) results without requiring their continuity. To support our findings, we provide nontrivial illustrative examples of CFP in MGM-spaces. In addition, we create 3-D column graphs to validate the contraction conditions of four self-mappings in MGM-spaces. Furthermore, we apply the nonlinear integral equation (NIE) to determine the existence of a unique common solution to unify our CFP results in the said domain. Our hypothesis will be critical to the theory of fixed points. Our findings can be expanded and improved in various ways by employing multiple sorts of mappings in MGM-spaces with applications.