A Neutrosophic Participation Quadruple Model for Analyzing Student Engagement in Blended Physical Education

Blended physical education (PE) integrates in-person and online activities, posing challenges in evaluating student engagement due to varying participation and uncertainties. This paper proposes a novel Neutrosophic Participation Quadruple (NPQ) model to assess engagement in college blended physical education (PE) courses. The model extends neutrosophic sets by adding a fourth component called “extended neutrality” to represent partial participation. It also uses topological structures to analyze engagement levels. We provide clear definitions, proven theorems, and a detailed case study. Compared to other methods, the NPQ model is better at handling uncertainty and partial engagement, giving educators a useful tool to improve teaching.