A Neutrosophic Probabilistic Distribution Framework for Modeling Uncertainty in Political Learning Environments: Precision Delivery Models Evaluation for College Political-Ideological Education

Abstract

In political education, uncertainty is inherent due to conflicting ideologies, ambiguous 
content, and subjective learner interpretations. Classical probability and statistical tools 
fail to fully represent this complexity. This paper introduces a novel Neutrosophic 
Probabilistic Distribution Framework (NPDF) for modeling uncertain phenomena using 
truth, indeterminacy, and falsity dimensions. Random variables are defined as 
neutrosophic-valued triplets, and new definitions for Neutrosophic Probability Density 
Functions (NPDFs), Neutrosophic Cumulative Distributions (NCDFs), Neutrosophic 
Expectation, and Neutrosophic Variance are proposed. A generalized Neutrosophic 
Bayes’ Theorem is also developed to support dynamic belief updating under uncertainty. 
The framework is applied to analyze bias and comprehension in digital political 
education. Results demonstrate the model’s capacity to mathematically capture complex 
ambiguity, outperforming classical and fuzzy systems in high-uncertainty environments.

DOI: 10.5281/zenodo.16754518