Neutrosophic Hyper-Distributions for Modeling Teaching Reform and Practice Efficiency Analysis of University Thought and Political Curriculum in Digital Education Environments

This study applies the Neutrosophic Hyper-Distribution (NHD) framework to model thought and political orientation in digital education environments. NHDs extend classical probability and neutrosophic logic by embedding full neutrosophic distributions within each truth (T), indeterminacy (I), and falsehood (F) component, enabling the capture of layered uncertainties and internal contradictions in belief structures. We formalize the Neutrosophic Hyper-Probability Density Function (NHPDF) and derive associated measures Hyper-Expectation, Hyper-Variance, and Hyper-Entropy—then apply them to a 12-week online political science course comparing moderated and unmoderated discussion groups. Data from weekly stance surveys, certainty ratings, and text analysis of discussion posts are mapped to NHD components. Results show that moderation supports a mild positive stance shift, reduces opinion variance, and lowers hyper-entropy, indicating more coherent and stable beliefs. In contrast, unmoderated discourse increases both variance and entropy, reflecting greater indecision and fragmentation. These findings demonstrate the value of NHDs as a quantitative tool for capturing the multi-layered cognitive and political effects of discussion strategies, offering educators a means to foster balanced and resilient political thinking in digital learning contexts.