A Hybrid Mathematical Modeling Approach for Analyzing Educational Decision-Making and Learning Behaviors in Digital Learning Environments

Abstract

Digital learning environments generate vast and continuous streams of behavioral data that capture how learners navigate content, allocate time, and respond to instructional stimuli. Understanding and predicting learner decision-making within such environments requires modeling frameworks capable of representing sequential choice, uncertainty, and multi-criteria evaluation simultaneously. This paper proposes a hybrid mathematical modeling framework that integrates a Markov Decision Process (MDP) for sequential learning-path decisions, a Fuzzy Cognitive Map (FCM) for representing the uncertainty inherent in learner behavior, and a probabilistic regression component for engagement estimation, combined through a weighted decision-fusion function. The hybrid model is formulated with explicit state-transition, membership, utility, and optimization equations, and is evaluated against single-technique baselines using accuracy, engagement index growth, and decision-consistency metrics on a simulated digital-learning dataset. Experimental results indicate that the hybrid model achieves a prediction accuracy of 91.6%, outperforming individual Markov, fuzzy, and regression-only baselines by 13.1–17.4 percentage points, while also producing a smoother and more sustained engagement trend across ten learning sessions. The findings demonstrate that combining stochastic, fuzzy, and statistical reasoning yields a more robust description of educational decision-making than any single paradigm, offering a practical foundation for adaptive learningpath recommendation systems in e-learning platforms. Keywords: Hybrid mathematical modeling; Markov Decision Process; Fuzzy Cognitive Map; digital learning environment; educational data mining; learner engagement; decision-making analytics.