Fuzzy rough graphs via fuzzy graph ideals with applications

In this paper, we extend the concept of fuzzy rough sets to graphs by introducing the notion of "fuzzy graph ideals". This novel approach enables the construction of rough fuzzy digraphs, termed "fuzzy graph ideal approximation spaces", along with associated methods of formation. We define new fuzzy lower and upper graphs based on any two fuzzy binary relations on the vertex and edge sets of a directed graph thereby utilizing the concept of fuzzy graph ideals. Additionally, we explore fuzzy interior and fuzzy closure graphs within rough fuzzy graphs, and examine properties such as fuzzy graph connectedness through the application of these new operators. These developments offer valuable tools to address uncertain decision-making problems, with potential practical applications in various domains. Particularly, we provide an algorithm to solve decision-making problems regarding the identification of the best location in a department to set a mobile phone Jammer.