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

Abstract

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. 

DOI: 10.5281/zenodo.15733497