Single-Valued Neutrosophic Hyperring Statistical Consistency Framework for Evaluating University Ideological and Political Education Quality

Abstract

Assessing the quality of ideological and political education at the university level requires 
handling diverse indicators, including knowledge acquisition, student participation, 
engagement, and attitudinal development. These indicators are often uncertain, partially 
contradictory, and context-dependent. To address this complexity, we propose a Single
Valued Neutrosophic Hyperring Statistical Consistency Framework (SVN-HSCF), which 
integrates hyperalgebraic structures with neutrosophic statistics. Within this framework, 
each indicator is represented as a single-valued neutrosophic element embedded in a 
hyperring, allowing operations that generate sets of outcomes rather than fixed results. 
We introduce the hyperbarycenter operator to define canonical averages and extend it to 
measures of variance, covariance, and probability under hyperoperations. Building on 
these tools, we formulate the Neutrosophic Statistical Consistency Index (NSCI), a 
bounded and weight-adjustable metric that captures the interplay of truth-membership 
(achievement), indeterminacy-membership (uncertainty), and falsity-membership (error) 
across multiple datasets. To enhance stability, a hyperideal regularization functional is 
incorporated to suppress random fluctuations without compromising hyperring 
coherence. Furthermore, we establish a hyper-probabilistic maximum likelihood 
estimation (H-MLE) method for parameter inference and construct neutrosophic 
confidence intervals with concentration inequalities. 
Theoretical validation is provided through existence, uniqueness, and closure theorems, 
while a worked example based on hypothetical evaluation data illustrates the practical 
application of the framework. The results demonstrate that SVN-HSCF effectively reduces 
measurement noise, preserves algebraic consistency, and yields interpretable department
level quality scores aligned with the NSCI. This approach offers a mathematically rigorous 
and adaptable tool for advancing decision-making in complex educational quality 
assessment contexts. 

DOI: 10.5281/zenodo.16934485