A Neutrosophic Locality-Based Algebraic Model for Evaluating  Teaching Quality in Music and Dance Classes: Hybrid Human  Performance as a Multidimensional Entity

Yuxi Guo; Yue Zhang

Authors

Yuxi Guo Qinhuangdao Vocational and Technical College, Qinhuangdao, China
Yue Zhang Qinhuangdao Vocational and Technical College, Qinhuangdao, China

Keywords:

Neutrosophic logic, teaching evaluation, music education, dance pedagogy, partial locality, hybrid identity, performance modeling, fuzzy algebra, uncertainty in education.

Abstract

Evaluating the teaching quality in music and dance classes is a complex task. It
involves both technical precision and emotional expression, often judged with incomplete
or conflicting observations. Traditional evaluation methods rely on fixed scores or binary
decisions, which fail to capture the fluid and hybrid nature of human performance. This
paper presents a new model that uses neutrosophic logic and algebra to evaluate music
and dance teaching. We treat each teaching moment as a hybrid act, with three degrees:
how clearly the skill is shown (truth), how uncertain the observation is (indeterminacy),
and how much the skill is missing (falsity). These are mapped into a structured space and
combined using an algebraic law that respects local teaching contexts. The model
introduces a locality-aware composition of evaluations, supported by mathematical
constraints and fully explained through examples. A complete case study is provided
from a dance composition class, using real teaching skills and step-by-step calculations.
The model is also compared with traditional evaluation methods, showing that it can
better reflect ambiguity and blended performance. This approach offers a flexible and
mathematically grounded way to evaluate hybrid human teaching acts, especially in the
expressive fields of music and dance.