Neutrosophic Co-Creative Quality Integral for College Interactive Music Teaching: A Multimodal Measurement and Bidirectional Bound Integration Framework

Abstract

This paper introduces a novel Neutrosophic Co-Creative Quality Integral (NCQI) 
designed for the quantitative evaluation of college-level interactive music teaching 
sessions. The proposed framework models teaching–learning interactions as a 
multimodal neutrosophic quality field, where each event is represented by a truth (T), 
indeterminacy (I), and falsity (F) component derived from heterogeneous input streams 
such 
as audio, MIDI scores, motion capture, and in-class responses. 
A neutrosophic quality measure is defined with explicit multimodal overlap correction, 
ensuring σ-additivity and eliminating double counting across correlated modalities. 
To address temporal uncertainties in interactive sessions, a bidirectional-bound 
neutrosophic integral is developed, integrating over intervals with uncertain start and end 
boundaries and incorporating this boundary uncertainty directly into the indeterminacy 
component. Additionally, refined neutrosophic probability distributions are employed to 
map micro-level performance criteria such as rhythmic accuracy, harmonic consonance, 
and response latency into the unified quality measure. Theoretical properties of the 
framework, including additive consistency and uncertainty bounds, are proven. 
A detailed case study demonstrates the computation of NCQI from real-time performance 
logs, showing its ability to separate high-quality engagement from temporal noise and 
multimodal ambiguity. This approach provides a mathematically rigorous, pedagogically 
interpretable, and computationally implementable methodology for assessing interactive 
music teaching quality in ways not previously reported in the literature. 

DOI: 10.5281/zenodo.16934623