Neutrosophic Stochastic Efficiency Modeling for Digital Pedagogy: A Geometric Brownian–Ornstein–Uhlenbeck Framework for Evaluating University Ideological–Political Course Teaching Reform and Practice Efficiency

Abstract

This study introduces a novel neutrosophic stochastic framework to assess the 
efficiency of digital pedagogy reforms in university Ideological and Political (I&P) 
courses. By integrating Neutrosophic Geometric Brownian Motion (NGBM) for modeling 
truth/benefit dynamics and Neutrosophic Ornstein–Uhlenbeck (N-OU) processes for 
indeterminacy and shortfall, we construct a triad (T, I, F) for each course. The framework 
ensures mathematical well-posedness and maps seven digital pedagogy indicators—
spanning delivery quality, engagement, and resource openness—to stochastic 
parameters. A scalar Neutrosophic Pedagogy Efficiency Index (NPEI) is derived, 
incorporating penalties for persistent ambiguity. Applied to five I&P course modules 
(IPT-Core, Marxism, Situation&Policy, Ethics&Law, ModernHistory), the model yields 
closed-form expectations, variances, and robust efficiency rankings. Results highlight IPTCore’s superior performance (NPEI = 0.489) and Ethics&Law’s challenges (NPEI = 0.189), 
driven by variations in benefit growth and ambiguity. This approach advances 
neutrosophic probability applications in educational evaluation, offering a scalable tool 
for policy analysis and reform optimization.

DOI: 10.5281/zenodo.17037033