Directed rough fuzzy graph with application to trade networking

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