Neutrosophic SuperHyperfunction Invariants for Teaching Quality  in College Big Data Programs

Junke Zheng; Ying Wang

Authors

Junke Zheng Xinxiang Institute of Engineering, Xinxiang, Henan, 453700, China
Ying Wang Xinxiang Institute of Engineering, Xinxiang, Henan, 453700, China

Keywords:

neutrosophic superhyperfunction; n-th powerset; superhyperaggregation; NET group action; Burnside invariant; fixed points and orbits; teaching quality; Big Data programs; track-level rollup; symmetry robustness; truth–indeterminacy–falsity (T–I–F).

Abstract

College Big Data programs organize teaching and assessment through many nested
layers items within modules, modules within courses, courses within tracks, and tracks
within the program while being exposed to routine perturbations such as grader swaps,
time-slot changes, and delivery-format shifts. This paper presents a symmetry-aware,
neutrosophic framework that models the academic hierarchy with superhyperfunctions
into the n-th powerset and evaluates teaching quality via a NET group action on the
evaluation space. A Burnside–Neutrosophic Quality Index (BNQI) is defined by
averaging fixed-set scores across the group, preserving truth (T), indeterminacy (I), and
falsity (F) through superhyperaggregation. We prove existence of the aggregate on finite
nests, establish bounds and invariance for BNQI, and show monotonic responses to
quality-improving changes. A fully calculated case study on three tracks (Data
Engineering, Data Science, Business Analytics) details the construction of the
superhyperfunction, the choice of NET generators, and the computation of track- and
program-level BNQI. Results reveal which signals of quality persist under admissible
permutations and where uncertainty and error concentrate, offering an interpretable,
stable basis for course review, track oversight, and program planning.