Abstract
Domination and its associated concepts are significant ideas in fuzzy graph theory that have applications in diverse fields such as neural networks, game theory, and telecommunication. This study presents the notions of dominance and its associated research in a broader form of fuzzy graph called the multidimensional fuzzy graph. Basic results, such as the relationship between these parameters and vertices, edges, minimal sets, and so forth, are identified and illustrated with appropriate examples. The dominance number of multidimensional fuzzy graphs is determined after undergoing operations such as direct product, tensor product, composition, join, and others. Ultimately, this study displays a decision-making problem that can be efficiently addressed by utilizing the concept of the dominance number. The effectiveness of this approach is then compared to various models, like [Formula: see text]-polar fuzzy sets.
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