Application of Picture Fuzzy Bondage Set to Find Least Crowded Passenger-Friendly Railway Division in India

Abstract Picture fuzzy graph is a relevant mathematical tool for describing our uncertain daily life events due to unpredictable and ambiguous information. In this paper, the idea regarding picture fuzzy bondage and non-bondage sets has been introduced. Some operations on picture fuzzy bondage and non-bondage sets, like union, intersection, complement, join, and direct sum, have been described. Also, we present some theorems regarding these operations. This study presents the notion of picture fuzzy bondage number, picture fuzzy non-bondage number, and their properties. We have proposed an algorithm to determine the picture's fuzzy bondage number. Finally, an application in the communication network has been proposed for finding less crowded passengers-friendly railway divisions on Indian Railway.