Directed rough fuzzy graph with application to trade networking

In the realm of linking networks to the real world, connectivity (strength of connectedness) plays a crucial role. In this article, we introduce three types of vertices based on the indegree and outdegree of the vertices of directed rough fuzzy networks (DRFNs). We also define the concept of strength-reducing sets (SRSs\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {SRS}s$$\end{document}) of DRF-vertices, DRF-edges, and important related results using the strongest path in directed rough fuzzy graphs (DRFGs). We generalize the idea of Menger’s theorem of vertices and edges in directed fuzzy graphs to directed rough fuzzy graphs which are appropriate for dealing with uncertainty in information systems. Furthermore, we use α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} strong DRF-edges, β\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta $$\end{document} strong DRF-edges and δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta $$\end{document} DRF-edges to identify developing countries most affected by trade deficits during COVID-19. Finally, our research results are compared with existing methods to demonstrate their applicability and productivity.