A new approximation technique based on central bodies of rough fuzzy directed graphs for agricultural development

The identification of central body in directed networks is critical as it shows the areas of the network that require attention by cutting through noisy data. In network theory, the measures of centrality offer numbers or values to nodes within a graph related to their network location. Many centrality measures already exist in different network models. However, these centrality measures are generally based on membership values of edges, and there is no widely acknowledged method to assess the efficacy and reliability of these measures when dealing with incomplete and ambiguous information concurrently. Therefore, we suggest an innovative perspective where centrality measures are introduced in rough fuzzy directed (RFD) network model that is a predominant approach for dealing incomplete and ambiguous information simultaneously. Based on the connectedness of the RFD network, the in-degree centrality \(C_{id}\) $C_{\mathit{id}}$ , out-degree centrality \(C_{od}\) $C_{\mathit{od}}$ , in-closeness centrality \(C_{ic}\) $C_{\mathit{ic}}$ and out-closeness centrality \(C_{oc}\) $C_{\mathit{oc}}$ are defined and characterized for its bounds. Expressions for centrality measures of rough fuzzy directed path networks and rough fuzzy directed cycle networks are generalized. Finally, this conceptual structure is applied to the decision-making of effective management of water supply system and it is used to assess and compare different approaches. The traditional centrality measures are found to perform poorly on a large number of networks, indicating inherent limits for expressing the centrality of nodes in complicated networks.