A Refined Neutrosophic Quad-Topological Framework for Evaluating University Physical Education Teaching Quality from the Student Experience Perspective

Abstract

In an era where the evaluation of university teaching quality increasingly depends on 
subjective, ambiguous, and often contradictory student feedback, classical evaluation 
models fall short in capturing the true complexity of the student experience. This paper 
introduces a novel and entirely original analytical framework based on refined 
neutrosophic topological structures, aiming to model and interpret the multidimensional 
nature of student perceptions in physical education courses at the university level. 
We propose a Refined Quadripartitioned Neutrosophic Topology (RQNT), which models 
each student’s learning experience as a topological object defined by four distinct 
components: satisfaction (T), contradiction (C), uncertainty (U), and rejection (F). This 
representation surpasses traditional fuzzy and binary models by capturing nuanced 
dynamics such as emotional ambivalence, perceptual ambiguity, and cognitive 
dissonance. A new neutrosophic learning surface is then constructed from student data, 
revealing topological zones of pedagogical strength, failure, and indeterminacy. 
The framework is applied to a comprehensive case study involving student feedback on 
physical education instruction across multiple universities. The results reveal deep 
structural insights into how students experience instructional quality, identify latent 
contradiction clusters, and suggest targeted pedagogical improvements. This is the first 
known application of neutrosophic topological methods to educational experience 
analysis, offering a new direction for data-driven educational diagnostics.

DOI: 10.5281/zenodo.16934797