The paper addresses speeding up meetings in a networked environment during rescue works in a transport emergency. Several groups of representatives of various services and observers participate in those meetings. The number of wrong decisions tends to increase because remote participants cannot understand each other quickly. First, the meetings must be efficiently held to avoid making wrong decisions, including medical diagnoses for injuries. The ultimate goals are to improve injured' health and life. Artificial intelligence (AI), big data analysis, and deep learning methods suggested in this paper for decisionmaking support have a cognitive character, i.e., try to take into account the thoughts and emotions of participants. The author's convergent approach ensures the purposefulness and sustainability of decision-making. This approach transforms divergent decision-making processes into convergent. The approach is based on the inverse problem-solving method in topological space, genetic algorithms, control thermodynamic theory, and using the ideas of creating AI models' cognitive semantics with quantum mechanics methods. This approach gives meetings' members the list of decision-making rules with accelerating consensus achievement. The examples of the rules are: the goals have to be arranged as a 3-level tree and ordered by importance; semantic interpretations of computer models’ factors and their connections must be separated; rescue resources must be represented in a finite number of separated components, and so on. The approach also exploits traditional technical tools of augmented reality, virtual collaboration, and situational awareness. It has been repeatedly used to build socioeconomic and manufacturing sectoral strategies and is currently being adapted for emergencies