Tasks of emergency evacuation planning on dynamic networks in fuzzy conditions are becoming ubiquitous because of the imprecise time-dependent nature and arguments of network. Underlying basis for evacuation tasks are different types of flow algorithms. The paper aims to present the urgent problem of artificial intelligence, namely, the development of a method for finding the optimal evacuation plan in a transportation network in fuzzy conditions as the universal flow problem. The proposed method consists in transporting the maximum number of aggrieved in each time interval based on finding the maximum flow of the earliest arrival in a fuzzy dynamic transportation network. The process of flow conveying is implemented on the network with time-dependent parameters. The main contribution of this paper is to propose a method operating arc capacities and traversal times that can vary depending on the flow departure time and are represented in a fuzzy form. Technique of blurring fuzzy numbers is represented to facilitate calculations. A case-study in the area of Bolshoi Theatre Moscow, Russia and surroundings is conducted to illustrate proposed algorithm. Experiments on the designed network were conducted to check resistance of the network to topology changes.