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The study of the mechanism for the development of mass panic in view of its extreme importance and social danger is an important scientific task. Available information about the mechanism of her development is based mainly on the work of psychologists and belongs to the category of inaccurate. Therefore, the theory of fuzzy sets has been chosen as a tool for developing a mathematical model of a person's susceptibility to panic situations. As a result of the study, an fuzzy model was developed, consisting of blocks: “Fuzzyfication”, where the degree of belonging of the values of the input parameters to fuzzy sets is calculated; “Inference” where, based on the degree of belonging of the input parameters, the resulting function of belonging of the output value to an odd model is calculated; “Defuzzyfication”, where using the center of gravity method, the only quantitative value of the output variable characterizing a person's susceptibility to panic situations is determined Since the real quantitative values for linguistic variables mental properties of a person are unknown, then to assess the quality of the developed model, without endangering people, it is not possible. Therefore, the quality of the results of fuzzy modeling was estimated by the calculated value of the determination coefficient R2, which showed that the developed fuzzy model belongs to the category of good quality models $(R^2 = 0.93)$, which confirms the legitimacy of the assumptions made during her development. In accordance with to the results of the simulation, human susceptibility to panic situations for sanguinics and cholerics can be attributed to “increased” (0.88), and for phlegmatics and melancholics — to “moderate” (0.38). This means that cholerics and sanguinics can become epicenters of panic and the initiators of stampede, and phlegmatics and melancholics — obstacles to evacuation routes. What should be taken into account when developing effective evacuation measures, the main task of which is to quickly and safely evacuate people from adverse conditions. In the approved methods, the calculation of normative values of safety parameters is based on simplified analytical models of human flow movement, because a large number of factors have to be taken into account, some of which are quantitatively uncertain. The obtained result in the form of quantitative estimates of a person's susceptibility to panic situations will increase the accuracy of calculations.

A mass congestion of people always represents a potential danger and threat for their lives. In addition, every year in the world a very large number of people die because of the crush, the main cause of which is mass panic. Therefore, the study of the phenomenon of mass panic in view of her extreme social danger is an important scientific task. Available information, about the processes of her occurrence and spread refers to the category inaccurate. Therefore, the theory of fuzzy sets has been chosen as a tool for developing a mathematical model of the mechanism of transmitting panic state among people with various temperament species.

When developing an fuzzy model, it was assumed that panic, from the epicenter of the shocking stimulus, spreads among people according to the wave principle, passing at different frequencies through different environments (types of human temperament), and is determined by the speed and intensity of the circular reaction of the mechanism of transmitting panic state among people. Therefore, the developed fuzzy model, along with two inputs, has two outputs — the speed and intensity of the circular reaction. In the block «Fuzzyfication», the degrees of membership of the numerical values of the input parameters to fuzzy sets are calculated. The «Inference» block at the input receives degrees of belonging for each input parameter and at the output determines the resulting function of belonging the speed of the circular reaction and her derivative, which is a function of belonging for the intensity of the circular reaction. In the «Defuzzyfication» block, using the center of gravity method, a quantitative value is determined for each output parameter. The quality assessment of the developed fuzzy model, carried out by calculating of the determination coefficient, showed that the developed mathematical model belongs to the category of good quality models.

The result obtained in the form of quantitative assessments of the circular reaction makes it possible to improve the quality of understanding of the mental processes occurring during the transmission of the panic state among people. In addition, this makes it possible to improve existing and develop new models of chaotic humans behaviors. Which are designed to develop effective solutions in crisis situations, aimed at full or partial prevention of the spread of mass panic, leading to the emergence of panic flight and the appearance of human casualties.