The article proposes a method for clarifying the degree of correspondence between the request of a company looking for a specialist for a vacant position and the request of an applicant. As practice shows, the requirements in the requests of companies and the requests of applicants are linguistic, using vague boundaries of compliance parameters. Based on the results of a survey of graduate students and representatives of potential employer companies conducted by the author of the work, the company’s image, its experience in the market, and a decent salary are significant for graduates. For potential employers, applicants with some experience in the branch and low financial expectations are substantial first of all. Thus, from the statements of both sides, the author managed to identify two linguistic variables: “Time” and “Salary level.” These variables are applied to identify correlations between requests at the preliminary stage of staff selection. Indirect methods, namely methods of statistical data and expert assessments, were used in the variable membership functions. The algorithm for detecting matches is noticeably simple and can be in almost any table processor, which expands the field of the proposed approach. The recruitment agency acts as an intermediary in recruitment. The algorithm for identifying compliance in its activities will significantly reduce recruiters’ time and labor costs.

In the context of growing and widespread demand for higher professional education, an important aspect is the quality of the educational process and the effectiveness of its results. The educational process is a complex socio-economic phenomenon involving at least two parties – the teacher and the students. It is these subjects of the process that are the key elements and interact, as a result of which there is an increase in the amount of information that is transformed into a competency-based form. It is the acquisition by students of the competencies they need in their professional activities that is the goal of the educational process. As a result of the study, it was found that it is possible to optimize the educational process and fill it with the necessary educational elements through fuzzy modeling of the transmission and perception of educational information. The article proposes a model of fuzzy interaction between a teacher and a student group. The model is designed to determine the possibilities of optimizing the educational process and the optimal combination of educational elements. Educational elements include teaching materials, communication tools, and digital technologies. With the help of these elements and the pedagogical strategy, the transfer of educational information to students is carried out. The same means and motivation are used for the perception of educational information. It is important to find the optimal combination of educational elements and tools that contribute to the effective transfer and assimilation of educational information. Improving the effectiveness of interaction between teachers and students affects the quality of education. The quality of the educational process determines the level of students' training, the success of graduates' professional activities, and the professional self-realization of teachers. The interaction model makes it possible to improve the quality of the educational process. This is confirmed by the results of its application at Tver State Technical University.