Neutrosophic Probabilistic and Statistical Extensions of the NeutroMultiSpace Model for Blended Teaching Process in University Physical Education: A Novel Neutrosophic Modeling Framework

This paper introduces a novel neutrosophic modeling framework to better understand and assess blended teaching in university physical education. The model is based on the NeutroMultiSpace structure, which combines in-person participation, digital engagement, and physical performance. Each of these dimensions is represented using neutrosophic triplets ⟨T, I, F⟩, reflecting levels of effectiveness, uncertainty, and failure. To make this model more realistic and practical, we extend it with new neutrosophic probabilistic and statistical tools. These include formulas to measure how well student performance fits the learning goals, as well as calculations of neutrosophic variance and confidence regions. These tools help identify differences between students and show how reliable the results are. This approach provides teachers with a powerful way to understand student learning on a deeper level. It captures not just what students get right or wrong, but also the uncertainty and flexibility that are part of real learning. The model is original in its foundation in neutrosophic logic and offers a new path for data-driven and personalized teaching in physical education and beyond.