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Domination in rough fuzzy digraphs with application


This manuscript expands the literature of domination theory of fuzzy graphs to rough fuzzy digraphs. The inaptness of the research on domination theory of fuzzy graphs to deal with real-life problems of complex networks with an information system containing indiscernibility and uncertainty requires introduction of domination theory to rough fuzzy digraph model which effectively deals and avoids constraints of fuzzy graphs in such networks. In the beginning, we define dominating set of a rough fuzzy digraph based on its lower and upper dominating sets and evaluate its domination number. We characterize bounds for the dominating set of rough fuzzy digraphs and analyze the behavior of the domination number on union, intersection and complement of rough fuzzy digraphs. Furthermore, we conceptualize rough fuzzy dipath graphs and rough fuzzy dicycle graphs and generalize expressions for computing their domination numbers. In addition, we demonstrate an application of dominating set in decision-making problem to select the best set of cities in a country that can supply a commodity to the whole country with minimum cost. Finally, we construct a framework and develop an algorithm which effectively tackles with decision-making problems concerning such complex networks.

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This manuscript is completed by both UA and TB. TB introduced the concept of domination and wrote this manuscript. UA designed the algorithm, analyzed the results and reviewed the manuscript. Both the authors read and approved the final manuscript.

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Correspondence to Uzma Ahmad.

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Ahmad, U., Batool, T. Domination in rough fuzzy digraphs with application. Soft Comput 27, 2425–2442 (2023).

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  • Rough fuzzy digraphs
  • Dominating set
  • Domination number
  • Rough fuzzy dipath
  • Rough fuzzy dicycle