Dual-Topology Linguistic Neutrosophic Filters for Teaching Quality Analysis in University Dance Aesthetic Education

Abstract

Assessing teaching quality in university dance aesthetic education demands methods that 
are precise, fair, and sensitive to style. This paper introduces a dual-topology, 
linguistically neutrosophic framework that represents each classroom event as a single
valued neutrosophic multiset and evaluates quality through two complementary lenses: 
a strict conjunctive topology that requires simultaneous compliance of multiple aesthetic 
attributes, and a permissive subbasic/disjunctive topology that allows acceptance when at 
least one attribute fully satisfies the rubric. We establish a stable information-technology 
pipeline by proving linguistic neutrosophic (semi-)continuity from raw sensors to scores, 
ensuring small measurement jitter cannot flip decisions. On top of this topology, we add 
an algebraic certification layer: acceptance sets form neutrosophic ℵ-filters, while minimal 
violations are captured as prime ℵ-bi-ideal witnesses that pinpoint the exact 
attribute/component (truth, indeterminacy, or falsity) needing improvement. We 
integrate both views into a normalized Topological Aesthetic Quality (TAQ) score that is 
monotone in the neutrosophic quality order, Lipschitz-robust, and invariant under 
admissible affine reparameterizations. An algorithm with linear complexity computes 
event- and sequence-level TAQ and certificates. A case study on classical and 
contemporary classes shows reproducible gains under averaging, predictable 
degradation under conservative composition, and clear, actionable diagnostics via prime
witness reporting. The result is an explainable, mathematically grounded approach to 
teaching quality analysis tailored to the nuanced realities of university dance aesthetics.

DOI: 10.5281/zenodo.16934790