A Neutrosophic Entropy-Based Statistical Model for Uncertainty Quantification in Mixed-Type Linguistic Data: Application to University Korean Language Teaching Management Innovation Evaluation

Abstract

Quantifying uncertainty in datasets that combine numerical and linguistic information 
poses a unique challenge to classical probabilistic frameworks, especially when 
ambiguity, vagueness, and partial truth are present. This paper introduces a novel 
statistical model grounded in neutrosophic entropy, built upon the triplet logic of truth 
(T), indeterminacy (I), and falsity (F). The model is applied to a hybrid dataset of 
University Korean language learners, integrating pronunciation scores and qualitative 
feedback to evaluate cognitive uncertainty. A new entropy formulation is derived and 
analyzed, with numerical experiments revealing that the neutrosophic entropy measure 
more accurately captures epistemic ambiguity than classical or fuzzy entropy. Results 
show distinct uncertainty profiles across learners, making the framework valuable for 
educational diagnostics and linguistic data modeling. 

DOI: 10.5281/zenodo.16754617