Upside-Down Neutrosophic Multi-Fuzzy Ideals for IT-Enhanced College Dance Teaching Quality Assessment

Abstract

This paper proposes a novel framework for evaluating the quality of college 
dance education in environments enhanced by information technology. The approach 
models dance performance data captured through motion sensors, video-based pose 
estimation, pressure-sensitive flooring, and audio beat-tracking as neutrosophic multi
fuzzy sequences (T,I,F)  that represent, respectively, the degree of technical accuracy, 
indeterminacy due to sensor noise or ambiguous movements, and deviations from the 
intended choreography. A pedagogical near-ring structure formalizes instructional 
operations such as tempo adjustment, camera viewpoint changes, and choreography 
resampling, while rubric ideals encode the acceptable performance boundaries for specific 
dance styles. Building on the concept of upside-down logic, we introduce Upside-Down 
Polarity Morphisms that reclassify certain deviations such as stylistic off-beat timing or 
deliberate imbalance as positive contributions to performance quality, depending on 
contextual cues. The final Quality-as-Ideal-Proximity metric computes the distance 
between a performance’s neutrosophic multi-fuzzy profile and its corresponding rubric 
ideal, adjusted by polarity morphisms. The framework is theoretically supported with 
proofs of closure, monotonicity, and stability, and its practical applicability is 
demonstrated through a case study using multimodal sensor data from contemporary and 
classical dance classes. 

DOI: 10.5281/zenodo.16934695