Covering of fuzzy graphs and its application in emergency aircraft landing using particle swarm optimization method

In graph theory, a set consisting of vertices of a graph that are incident to at least one of the edges is called a vertex covering set for that fuzzy graph. Facility location problems are represented as fuzzy graphs, and a model is designed with multi-objective optimization programming problems. These problems are solved using the Particle Swarm Optimization approach combined with the covering concept of fuzzy graphs. An algorithm is designed for finding fuzzy vertex covering set of fuzzy graphs. The definitions of covering speed, covering time, and coverage impact for a fuzzy vertex cover are introduced and used to develop the model. This model uses a fuzzy graph with vertices as demand and facility nodes. In case of a sudden change in the total demand of the system, there is a change in the fuzzy covering radius or capacity of facility nodes. The problem is to cover up the fuzzy network by placing facilities with maximizing demand and optimizing unknown fuzzy parameters. These studies solve a real-life problem: emergency aircraft landing with minimum time and nearest landing place. Also, the method minimizes the loss of aircraft and passengers. The proposed methodology is a new approach to solving such complex problems.