The object of the dissertation research is the process of reforming higher education in Ukraine. The purpose of the dissertation research is a system analysis of the organization of higher technical education at the university level and the ways of its reformation according to the ideology of duality in the conditions of the implementation of the online mode of teaching academic disciplines to justify the priority based on a set of criteria for evaluating the development process. During the dissertation the following research methods were used: methods of system analysis, catastrophe theory, neural and neurofuzzy networks, theory of differential equations, theory of fuzzy multicriteria optimization and theory of fuzzy logic. Theoretical results:for the first time, a variant of the priority of the selected criteria was proposed, and the best variant of the university's development plan was determined based on a vague set of their optimal values, which would contribute to the stable growth of its image from year to year; for the first time, the mathematical model of the process of forgetting the knowledge received at the lecture was modified. The system-transformed mathematical model is implemented in relative time and contains three main parameters, one of which characterizes the rate at which the student forgets the information received at the lecture, the second characterizes the synergistic component that slows down the forgetting process, and the third characterizes the component of the received information that remains in memory student forever; for the first time, a new mathematical model was synthesized that describes the process of assimilation by the student of the knowledge received at the lecture, at the beginning of which the lecturer restores the main points of the previous lectures in the students' memory in a concentrated form; for the first time, a new mathematical model of the intellectual state of society in the class of catastrophes was synthesized using a correctly written balance equation, which also takes into account the time period during which this balance is maintained, and it is proved that the function of the increase in the relative intelligence of society, the argument of which is the relative number of members of society contributing the contribution to this increase cannot have extrema in the range of values admissible for this argument; a fuzzy mathematical model for a clear assessment of the quality of the educational process and a methodology for assessing the quality of knowledge received by students in the online mode have been improved; the mathematical model of the "forgetting curve" created by H. Ebbinghaus has been improved, which takes into account both the synergistic component that slows down the process of forgetting due to the internal work of the brain during the period of time when new information does not reach the brain, and the component that sets the value of that fate of the initial information that is never erased from the individual's memory. The practical results consist in the development of an approach to the system planning of the development of the university based on a fuzzy variant of multi-criteria optimization, which allows, in the process of implementing the synthesized plan, to adapt it in case of achieving certain intermediate goals and to adapt a fuzzy mathematical model for a clear assessment of the quality of the educational process in the online mode and methods of its clear assessment on fuzzy models. The results obtained in the dissertation are recommended for implementation at Vinnytsia National Technical University and in scientific research, on the subject approved by the Department of Higher Education of the National Academy of Pedagogical Sciences of Ukraine.
