The globalization of the processes of the modern period of human development touches not only the economic relations of the countries, but also penetrates into other extremely sensitive aspects of human life, including the very fact of its existence. Such processes can be fully attributed to the modern stage of development of science, technology, engineering, which is followed by stormy, and sometimes explosive nature, which, in turn, leads to significant shifts in scientific research, engineering, pedagogy, psychology, sociology, etc. . The main feature of all these processes - their scale, mass, diversity, while covering a large number of diverse objects, both wild and non-living. The result of these processes, of course, cannot be predicted reliably, since any information on their course (which is becoming increasingly important today) will in any circumstances be characterized as incomplete and inaccurate, presented both numerically and non-numerically.

Modern research and prediction of these processes are largely related to three categories: probability, logic, fuzziness, which have become an integral part of professional activity in the fields of engineering, sociology, pedagogy, medicine, psychology, etc. After all, researching large systems, global processes inherent in the living and inanimate nature, specialists are faced with the need to make appropriate decisions, usually in the context of incomplete, inaccurate, not deterministic, often non-numerical information. In such circumstances, the application of well-developed classical methods of function theory and functional analysis to the study of relevant objects becomes limited, ineffective, and often impossible. At the same time, the concepts of probability, logic and fuzziness in the application of appropriate research tools in various fields of human activity today have many interpretations, each of which leads to success under well-defined conditions.

The above leads to the conclusion that in modern conditions the high school has a special responsibility for the proper content and methodological provision of the educational process for providing relevant knowledge to students of different specialties, directing the student to recognize what he will use in his professional activity, since deep penetration into the content applicable tools, allows the specialist to consciously relate not only to the subject of work, but also to their own thinking processes, to manage these processes, directing them to achieve the desired result. In the presented work in view of the tasks of higher education, the analysis of various interpretations and interpretations of the concepts of "probability", "logic", "fuzzy" is carried out, the general and different that is inherent in these concepts is revealed, the inevitability and objectivity of the concepts of mutual understanding are substantiated considering their possible application.