A Neutrosophic Deep Hyper-Algebraic Model for University Physical Education Teaching: A Multilayered Analytical Framework

Abstract

This paper introduces a novel mathematical framework titled the Neutrosophic Deep 
Hyper-Algebraic Model (NDHAM) designed to address the inherent indeterminacy, 
vagueness, and contradiction in university physical education teaching systems. Drawing 
inspiration from the superhyperstructures and neutrosophic algebraic formulations, the 
proposed model constructs an Nth-order neutrosophic hyper-powerset that encapsulates 
the evolving and multi-layered relationships among students, instructors, tasks, and 
environmental variables. This framework integrates neutrosophic truth (T), 
indeterminacy (I), and falsity (F) within a recursive algebraic structure, allowing each 
pedagogical unit to be expressed through a Deep Neutrosophic HyperTuple. 
The model introduces a new class of (m,n)-Neutrosophic Deep HyperOperations, 
generalized beyond classical group axioms, and further enriched by a parameterized 
Dombi-inspired aggregation mechanism to flexibly interpret individual and group 
performance under uncertainty. Applied to a university-level physical education setting, 
the model demonstrates the ability to quantify cognitive, behavioral, and physical 
engagement through dynamically adaptive neutrosophic evaluations. Comparative 
simulations show that the model outperforms traditional crisp or fuzzy decision systems 
by retaining high structural granularity and epistemic elasticity. 
This research opens new frontiers in the fusion of abstract algebraic structures and applied 
educational sciences, positioning neutrosophic theory as a powerful lens for analyzing 
complex instructional systems. 

DOI: 10.5281/zenodo.16934873