International Journal of Modern Education and Computer Science (IJMECS)

ISSN: 2075-0161 (Print), ISSN: 2075-017X (Online)

Published By: MECS Press

IJMECS Vol.14, No.4, Aug. 2022

Mathematical Model for Adaptive Technology in E-learning Systems

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Nataliia Barchenko, Volodymyr Tolbatov, Tetiana Lavryk, Viktor Obodiak, Igor Shelehov, Andrii Tolbatov, Sergiy Gnatyuk, Olena Tolbatova

Index Terms

Computer Science, E-Learning, Adaptation, Fuzzy Logic, Optimization, Mathematical Model.


The emergence of a large number of e-learning platforms and courses does not solve the problem of improving the quality of education. This is primarily due to insufficient implementation or lack of mechanisms for adaptation to the individual parameters of the student. The level of adaptation in modern e-learning systems to the individual characteristics of the student makes the organization of human-computer interaction relevant. As the solution of the problem, a mathematical model of the organization of human-computer interaction was proposed in this work. It is based on the principle of two-level adaptation that determines the choice of the most comfortable module for studying at the first level. The formation of an individual learning path is performed at the second level. The problem of choosing an e-module is solved using a fuzzy logic. The problem of forming a learning path is reduced to the problem of linear programming. The input data are the characteristics of the quality of student activity in the education system. Based on the proposed model the computer technology to support student activities in modular e-learning systems is developed. This technology allows increasing the level of student’s cognitive comfort and optimizing the learning time. The most important benefit of the proposed approach is to increase the average score and increase student satisfaction with learning.

Cite This Paper

Nataliia Barchenko, Volodymyr Tolbatov, Tetiana Lavryk, Viktor Obodiak, Igor Shelehov, Andrii Tolbatov, Sergiy Gnatyuk, Olena Tolbatova, "Mathematical Model for Adaptive Technology in E-learning Systems", International Journal of Modern Education and Computer Science(IJMECS), Vol.14, No.4, pp. 1-15, 2022.DOI: 10.5815/ijmecs.2022.04.01


[1]Grif M. G., Sundui, O., Tsoy, E. B. “Methods of designing and modeling of man-machine systems”, Proceedings of International Summer workshop Computer Science. pp. 38-40, 2014. 

[2]Omid. Sharifi, "Score-Level-based Face Anti-Spoofing System Using Handcrafted and Deep Learned Characteristics", International Journal of Image, Graphics and Signal Processing (IJIGSP), Vol.11, No.2, pp. 15-20, 2019.DOI: 10.5815/ijigsp.2019.02.02

[3]Pinchuk, O., Burov, O., Lytvynova, S. “Learning as a systemic activity”, Karwowski W., Ahram T., Nazir S. (Eds.), Advances in Human Factors in Training, Education, and Learning Sciences. Springer, Cham, pp. 335-342, 2020. DOI: 10.1007/978-3-030-20135-7_33.

[4]Zaritskiy, O., Pavlenko, P., Tolbatov, A. “Data representing and processing in expert information system of professional activity analysis”, 2016 Modern Problems of Radio Engineering, Telecommunications and Computer Science, Proceedings of the 13th International Conference on TCSET, pp. 831–833.

[5]Zaritskry, O., Pavlenko, P., Sudic, V., Tolbatov, A., Tolbatova, O., Tolbatov, V., Tolbatov, S., Viunenko, O. “Theoretical bases, methods and technologies of development of the professional activity analytical estimation intellectual systems”, 2nd International Conference on Advanced Information and Communication Technologies, pp. 101-104, 2017.

[6]Ennouamani, S., Mahani, Z. “An overview of adaptive e-learning systems”, Eighth International Conference on Intelligent Computing and Information Systems (ICICIS), Cairo, pp. 342-347, 2017. DOI: 10.1109/INTELCIS.2017.8260060.

[7]Klašnja-Milićević A., Vesin B., Ivanović M., Budimac Z., Jain L.C. “Personalization and adaptation in e-learning systems”, E-Learning Systems. Intelligent Systems Reference Library, pp. 21-25, 2017. DOI:10.1007/978-3-319-41163-7_1.

[8]Fleming, S., McKee, G., Huntley-Moore, S. “Undergraduate nursing students' learning styles: a longitudinal study”, Nurse education today, 31(5), pp. 444–449, 2011. DOI: 10.1016/j.nedt.2010.08.005.

[9]Knoll, A. R., Otani, H., Skeel, R. L., Van Horn, K. R. “Learning style, judgements of learning, and learning of verbal and visual information”, British journal of psychology, 108(3), pp. 544–563, 2017.

[10]Fleming, N., Baume, D. “Learning Styles Again: VARKing up the Right Tree!”, Educational Developments, 7, pp. 4-7, 2006.

[11]Mabrouk, M. El, Gaou, S. and Rtili, M. K. “Towards an intelligent hybrid recommendation system for e-learning platforms using data mining,” International Journal of Emerging Technologies in Learning (iJET), 12(06), pp. 52-76, 2017.

[12]Ehimwenma, K.E., Crowther, P., Beer, M. Formalizing logic based rules for skills classification and recommendation of learning materials. I.J. Information Technology and Computer Science, 9, pp. 1-12, 2018.

[13]Rawat, B., Dwivedi, S.K. An Architecture for Recommendation of Courses in E-learning System, I.J. Information Technology and Computer Science, 4, pp. 39-47, 2017. DOI: 10.5815/ijitcs.2017.04.06

[14]Mitra, M., Das, A."A Fuzzy Logic Approach to Assess Web Learner's Joint Skills", IJMECS, 7, 9, pp.14-21, 2015.DOI: 10.5815/ijmecs.2015.09.02

[15]Muhammad, A., Zhou, Q., Beydoun, G., Xu, D., Shen, J. “Learning path adaptation in online learning systems”, IEEE 20th International Conference on Computer Supported Cooperative Work in Design (CSCWD), pp. 421-426, 2016. DOI: 10.1109/CSCWD.2016.7566026.

[16]Dai, J., Su, G., Sun, Y., Ye, S., Liao, P., Sun, Y. “Application of advanced Petri net in personalized learning”, Proceedings of the 9th International Conference on E-Education, E-Business, E-Management and E-Learning. Association for Computing Machinery, New York, NY, USA, pp. 1–6, 2018. DOI: 10.1145/3183586.3183588.

[17]Wang F., Zhang L., Chen X., Wang Z., Xu X. “Research on personalized learning path discovery based on differential evolution algorithm and knowledge graph”, Data Science. ICDS 2019. Communications in Computer and Information Science, 1179, Springer, Singapore, pp. 285-295, 2019. DOI: 10.1007/978-981-15-2810-1_28.

[18]Colchester, K., Hagras, H., Alghazzawi, D., Aldabbagh, G. “A survey of artificial intelligence techniques employed for adaptive educational systems within e-learning platforms”, Journal of Artificial Intelligence and Soft Computing Research, 7(1), pp. 47-64, 2017. DOI: 10.1515/jaiscr-2017-0004.

[19]Dovbysh, A., Budnyk, M., Piatachenko, V., Myronenko, M. “Information-Extreme Machine Learning of On-Board Vehicle Recognition System”, Cybernetics and Systems Analysis, 56, pp. 534–543, 2020. DOI: 10.1007/s10559-020-00269-y.

[20]Chen, Y. H., Tseng, C. H., Huang, C. L., Deng, L. Y., Lee, W. C. “Recommendation system based on rule-space model of two-phase blue-red tree and optimized learning path with multimedia learning and cognitive assessment evaluation”, Multimedia Tools and Applications, 76(18), pp. 18237–18264, 2017. DOI: 10.1007/s11042-016-3717-3.

[21]Gao, Y., Chang, H. J., & Demiris, Y. “Iterative path optimisation for personalised dressing assistance using vision and force information”, IEEE/RSJ international conference on intelligent robots and systems, Daejeon, pp. 4398-4403, 2016. DOI: 10.1109/IROS.2016.7759647.

[22]Vanitha, V., Krishnan, P., Elakkiya, R. “Collaborative optimization algorithm for learning path construction in E-learning”, Computers & Electrical Engineering, 77, pp. 325-338, 2019. DOI: 10.1016/j.compeleceng.2019.06.016.

[23]Zhengbing Hu, Ivan Dychka, Mykola Onai, Yuri Zhykin, "Blind Payment Protocol for Payment Channel Networks", International Journal of Computer Network and Information Security (IJCNIS), Vol.11, No.6, pp.22-28, 2019.DOI: 10.5815/ijcnis.2019.06.03

[24]Sisay Tumsa, " Application of Artificial Neural Networks for Detecting Malicious Embedded Codes in Word Processing Documents", International Journal of Wireless and Microwave Technologies (IJWMT), Vol.10, No.5, pp. 35-40, 2020.DOI: 10.5815/ijwmt.2020.05.04 

[25]Zhang, J. H., Xia, J. J., Garibaldi, J. M., Groumpos, P. P., Wang, R. B. “Modeling and control of operator functional state in a unified framework of fuzzy inference petri nets”, Computer Methods and Programs in Biomedicine, 144, pp. 147-163, 2017. DOI: 10.1016/j.cmpb.2017.03.016.

[26]Lavrov, E., Pasko, N., Tolbatov, A., Barchenko, N. “Development of adaptation technologies to man-operator in distributed e-learning systems”, 2nd International Conference on Advanced Information and Communication Technologies, pp. 88-91, 2017. DOI: 10.1109/AIACT.2017.8020072.

[27]Lavrov, Е., Barchenko, N., Pasko, N., Borozenec, I. “Development of models for the formalized description of modular e-learning systems for the problems on providing ergonomic quality of human-computer interaction”, Eastern-European journal of enterprise technologies, 2, pp. 4-13, 2017. DOI: 10.15587/1729-4061.2017.97718.

[28]Lavrov, E., Barchenok, N., Lavrova, O., Savina, N. “Models of the dialogue “human-computer” for ergonomic support of e-learning”, ICTERI Workshops 2019 3rd International Conference on Advanced Information and Communications Technologies. pp. 187-190. DOI: 10.1109/AIACT.2019.8847763.

[29]Lavrov, E., Kupenko, O., Lavryk, T., Barchenko, N. “Organizational approach to the ergonomic examination of e-learning modules”, Informatics in education, 12(1), pp. 107-124, 2013. DOI: 10.15388/infedu.2013.08.

[30]Lavrov, E., Lavrova, O. “Intelligent adaptation method for human-machine interaction in modular e-learning systems”, Proceedings of the 15th International Conference on ICT in Education, Research and Industrial Applications. Integration, Harmonization and Knowledge Transfer. Volume II: Workshops, 2019. 

[31]Adamenko, A.N., et al. Informatsionnye upravlyayushchye cheloveko-mashynnye sistemy issledovanyia, proektyrovanye, testyrovanye (Information controlling human-machine systems: research, design, and testing). Mashinostroyenye, Мoscow, 1993.

[32]Giurgiu, L. “Microlearning an evolving elearning trend”, Scientific Bulletin, 22(1), pp. 18-23, 2017. DOI: 10.1515/bsaft-2017-0003.

[33]Siwi, M. K. Yuhendri L V. “Analysis Characteristics of Learning Styles VAK (Visual, Auditory, Kinesthetic) Student of Banks and Financial Institutions Course”, International Conference on Education for Economics, Business, and Finance (ICEEBF), 2016.

[34]Zhengbing Hu, Yulia Khokhlachova, Viktoriia Sydorenko, Ivan Opirskyy, "Method for Optimization of Information Security Systems Behavior under Conditions of Influences", International Journal of Intelligent Systems and Applications (IJISA), Vol.9, No.12, pp.46-58, 2017. DOI: 10.5815/ijisa.2017.12.05