(untitled) (European Journal of Pure and Applied Mathematics, 2025)
In graph theory, dominance has been a key idea for examining influence, control, and optimization in various systems. By examining domination in rough m-polar fuzzy digraphs—a hybrid model that combines directed graphs, m-polar fuzzy logic, and rough set theory—this work presents a fresh expansion of this idea. This structure makes it possible to simulate multi-polar decision contexts, uncertainty, and imprecision in a single framework. We justify the requirement for a more sophisticated concept of domination in rough m-polar fuzzy digraphs by first going over the fundamental concepts behind them. After a formal definition of domination in this context is put forward, its basic characteristics and structural ramifications are thoroughly examined. After that, the study concentrates on two crucial operations: the strong product of rough m-polar fuzzy digraphs and the tensor product. We characterize these procedures in the new framework and examine their effects on the resulting graphs’ dominating parameters. Under multi-valued and uncertain circumstances, these operations help to generalize the relationships and interactions amongst intricate network topologies. A thorough numerical example is given to illustrate the suggested notions’ applicability in real-world situations. Lastly, the use of domination in rough m-polar fuzzy digraphs is examined, emphasizing its potential in practical contexts like information systems, social network analysis, and uncertain decision-making. The study’s conclusions open up new possibilities for using domination theory in dynamic and unpredictable contexts and further the theoretical development of fuzzy and rough graph models.