Stochastic Neutrosophic Probability Fields for Modeling Temporal Uncertainty in Digital System for Ethnic Music Education and Inheritance

Abstract

 In this paper, we introduce a novel mathematical framework called Stochastic 
Neutrosophic Probability Fields (SNPF) designed to model the evolution of truth, 
indeterminacy, and falsity in time-varying cultural knowledge systems. While classical 
neutrosophic theory treats uncertainty as a static triplet of degrees, the SNPF approach 
redefines these components as stochastic functions of time, governed by differential and 
probabilistic dynamics. This allows for the modeling of how collective truth, ambiguity, 
and rejection shift in response to temporal, social, and cognitive fluctuations, particularly 
relevant in domains such as the international transmission of traditional Chinese ethnic 
music through digital media. We present formal definitions, derive foundational 
equations, prove theoretical properties, and illustrate the utility of the model in capturing 
the dynamic interplay between belief systems and cultural symbols. This work establishes 
a mathematically rigorous and application-driven expansion of neutrosophic logic. 

DOI: 10.5281/zenodo.16344382