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

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.