Mathematical modeling of the competency-based approach in education based on the theory of fuzzy sets

Abstract

The article considers a fuzzy-set approach to modeling a competency based approach in education at a technical university. A new methodology for assessing the level of formation of students’ competencies based on the results of certification by standard means has been developed. The proposed methodology is based on fuzzy-set aggregation of the results obtained when students solve various assessment tasks. Assessment tasks were selected from the appropriate sets recommended by experts to check the level of competency development, as well as selected by a particular teacher based on the proposed recommendations. The study used the apparatus of matrix data aggregation based on a system of fuzzy-logical inferences — standard fuzzy multilevel [0, 1]-classifiers that allow taking into account the significance (weight) of various types of assessment means and specific tasks.The developed algorithm makes it possible to calculate the proportion of students with the appropriate level of mastery of competencies in each of the areas of study in general, as well as in specific specialties separately. The subsequent fuzzification of the problem makes it possible to obtain recruitment estimates corresponding to the pessimistic, average expected, and optimistic forecasts, and thereby solve the problem of optimizing university recruitment, taking into account the real needs of the personnel market for a particular region.