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-polardecision 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 thesuggested 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.
Fahmi et al. (2025) studied this question.