The article discusses a method for determining the strong connectivity of a periodic fuzzy graph (PFG), which can be used to make decisions in emergency situations such as evacuation. The concept of a fuzzy set of strong connectivity is introduced. The main attention is paid to the development of a method for finding a fuzzy set of strong connectivity, which makes it possible to determine the degree of reachability between the vertices of a graph in a certain number of time cycles. The paper begins with a review of existing approaches to connectivity analysis in fuzzy graphs, emphasizing the need to consider time and fuzzy parameters. The main part of the paper is devoted to the description of key concepts and definitions related to periodic fuzzy graphs. The concepts of fuzzy path, time and degree of reachability, as well as fuzzy set of reachability are introduced. An algorithm for finding a fuzzy set of reachability based on the wave method is proposed, which allows determining the degree and time of reachability between graph vertices. Next, the concept of fuzzy set of strong connectivity PFG is introduced and an algorithm for its determination is proposed. As an example, a specific PFG is considered for which the fuzzy set of strong connectivity is calculated. The proposed method can be useful for choosing a movement strategy during evacuation, especially in conditions where the territory model is represented by a periodic fuzzy graph. In the future, it is planned to explore issues related to finding a discrete-time reachability between vertices with a given degree of reachability
