Authors - Natalya Aleynikova, Anna Loskutova, Mikhail Matveev, Elena Sviridova Abstract - The paper solves the problem of controlling the states of a system that may exhibit prolonged transient processes. As an example, the learning process of students is considered. Control is carried out based on predicting the dynamics of student academic performance. Academic performance – one of the key indicators of learning quality – is typically measured on graded scales and represented, for instance, by time series of student grades (scores). Instead of traditional time series analysis of grades, the present paper proposes transitioning to a space of fuzzy states (categories): “Fail”, “Satisfactory”, “Good”, and “Excellent”. The dynamics of these fuzzy categories are described using a discrete-time Markov chain model with fuzzy states, analyzing not the current but the limiting (steady-state) distributions of a student’s states. The paper presents a recurrent algorithm for the transition from the space of numerical grades to the space of fuzzy states, constructing the stochastic matrix of the Markov chain. The properties of the stochastic matrix are investigated to determine the existence and uniqueness of the limiting state distributions. Additionally, an approach is proposed for identifying change points – the moments when a shift in a student’s performance trend occurs.
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