Mathematical Model of E-learning System Based on Fuzzy Logic

Authors

  • Vadym Mukhin
  • Valerii Zavhorodnii
  • Viacheslav Liskin
  • Sergiy Syrota
  • Ganna Zavhorodnia

Keywords:

e-learning system, fuzzy logic, intelligent educational systems, modeling of student success

Abstract

One of the key challenges of modern e-learning is the timely identification of students at risk of expulsion in conditions of uncertainty and incompleteness of input information. The purpose of this work is to develop a mathematical model of e-learning system based on fuzzy logic that can predict the probability of successful completion of the course.

The proposed model considers key factors of academic success, such as activity, time spent in the system, average score, attendance, participation in discussions, and test scores. To process input data, triangular belonging functions and a fuzzy rule base are used to formalize uncertainty in educational data. The centroid method is used as a defuzzification method.

The paper formulates and solves the problem of predicting the expulsion of students using an adaptive neuron-fuzzy system. A numerical experiment was conducted on the data of 1000 students, during which the classification accuracy of 81.7% and the value of AUC = 0.90 were achieved, which confirms the high efficiency of the model.

The practical significance of the proposed approach lies in the possibility of its integration into existing e-learning systems for the early identification of students at high risk of academic failure and subsequent adaptive management of the educational process aimed at reducing expulsions and increasing the effectiveness of e-learning.

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Published

2026-03-31

How to Cite

Mukhin, V., Zavhorodnii, V., Liskin, V., Syrota, S., & Zavhorodnia, G. (2026). Mathematical Model of E-learning System Based on Fuzzy Logic. International Journal of Computing, 25(1), 48-55. Retrieved from https://www.computingonline.net/computing/article/view/4487

Issue

2026, Volume 25, Issue 1

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