Construction and Analysis of Neutrosophic Regression Models Under Triple Uncertainty (T, I, F): A Statistical Framework for Modeling Learning Outcomes in College Japanese Classrooms

Abstract

This paper introduces a novel neutrosophic regression model designed to 
analyze educational data within college Japanese classrooms, where outcomes are often 
affected by incomplete, uncertain, or ambiguous factors. The model operates in a triplet
valued space, representing each observation by its degrees of truth (T), indeterminacy (I), 
and falsity (F). We formally construct the neutrosophic regression function using 
extended arithmetic over these triplets and define a new method of least squares 
estimation within the neutrosophic domain. By applying the model to classroom 
assessment data where student performance may be influenced by latent variables such 
as cultural hesitation, test anxiety, or implicit learning, we demonstrate how traditional 
regression fails to capture the full informational uncertainty. The paper provides rigorous 
mathematical definitions, neutrosophic variance and covariance structures, full 
derivations, and a detailed numerical case study. This framework enables more accurate 
modeling of learning processes where outcomes are not absolutely true or false, but 
partially indeterminate, offering a powerful statistical tool for education systems dealing 
with epistemic ambiguity. 

DOI: 10.5281/zenodo.16754632