Fuzzy rough set is a hybrid tool for handling indeterminate, inconsistent and uncertain information that exist in real life. Graph theory has numerous applications in various disciplines, including modern sciences and technology, database theory, computer networks, expert systems and image capturing. In this paper, we apply fuzzy rough set theory to graph theory and investigate a new kind of graph structure which is called fuzzy rough digraphs. Then we describe some of their theoretical properties. Finally, we consider applications of fuzzy rough digraphs in decision-making to demonstrate the applicability, feasibility, effectiveness of the proposed algorithm.
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