Isites for the introduction of the fuzzyprobabilistic approach in the construction of mathematical models in personality psychology. The specificity of this field of psychology lies in the impossibility of constructing effective mathematical models by deterministic methods, including statistical ones. The fact is that statistical methods are intended for processing a variety of initial data and are used successfully in social psychology, which describes the trends of a certain phenomenon of a group of people «in general and in the middle», but are not applicable to an individual personality. The main position of the authors is the need to use the knowledge and experience of highly qualified specialistspsychologists who practice direct counseling of clients to solve personal psychological problems. The proposed apparatus for constructing fuzzy probability models is presented in the form of an algorithm that describes all the necessary steps – from working with an expert to interpreting models and using them to obtain qualitatively new information about the client's psychological state. The application of the fuzzyprobability approach is illustrated by the example of the synthesis of a mathematical model for assessing and predicting the psychological state of a woman's readiness to create a stable family

Security is always relevant, especially for particularly important objects. However at present the tasks of quantitative assessment of complex safety are solved, as a rule, locally for each object due to the absence of generalized methodology. At all fundamentality of statement of tasks of estimation of complex safety of especially important objects in regulating documents they have mainly declarative character. In this study we made an attempt to synthesize a mathematical model of quantitative assessment of integrated security of critical facilities on the basis of fuzzypossibility approach (FPL), using the knowledge and experience of experts. In this case, the methodology of FEA provides the representation of expert knowledge by fuzzy linguistic variables in a multidimensional factor space, followed by their formalization by a fuzzypossibility model.

Teachers always face problems when assessing the competence level of test participants (whether students, undergraduates, etc.) in both moral and psychological fields as well as methodological. This raises important questions on the creation of professional systems, which have mathematical models set forth for their vital foundational path. The current working method in the creation of mathematical models for evaluating the competency of test participants is based on a fuzzy logic approach using both the explicit and implicit knowledge of highly qualified experts. One can see the realisation of this method in the example of Englishlanguage instruction. A comparison of two common assessment scales for knowledge of the tested has been carried out – the «fivepoint » standard adopted in Russia (or required, actually) and the converted sevenpoint ECTS (European Credit Transfer and Accumulation System) rating scale which is based on percentage. This study has shown that teachers cannot effectively assess the participants’ competency, neither on individual topics nor on the course as a whole, due to the narrowness of the «fivepoint » scale.

Reindeer is part of the humandeerpasture sociobiological system, where all the constituent parts form emergence. The differences between the reindeer husbandry of foreign countries and Russia are shown. Reindeer in various countries are considered mainly as wild, few herds, and in Russia, at present, 75% of the reindeer population in the Arctic zone belongs to the domestic form. Therefore, the approaches to the study of the problems of reindeer husbandry also differ: the studies of foreign scientists are focused on the study and construction of models of local problems, while Russian studies, in addition to important local problems, are aimed at solving the problems of analyzing the features of the entry of traditional fishing farms into the system of market relations and forms adaptation of traditions to the modern image of economic reality. However, the description of sociobiosystems refers to poorly formalized problems that do not lend themselves to modeling by deterministic mathematical methods, and even more so by statistical ones. Therefore, a new fuzzypossibility approach for constructing multifactor models is proposed, based on the use of explicit and implicit knowledge and experience of experts. An example of constructing an adequate fuzzypossibility model of the stability of a reindeer husbandry in a sevenfactor space of both quantitative and nonquantitative (qualitative) variables is given. The adequacy of the model was confirmed situationally for the state of three reindeerbreeding commercial farms in the YamalNenets Autonomous Okrug for 2019 and 2020.

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