Students’ Innovation Ability Evaluation in Vocational Colleges Based on the STEAM Education Concept: A Neutrosophic SuperHyper Pentapartitioned Process Model

Abstract

Innovation ability is increasingly regarded as a core competence in vocational education, 
particularly under the STEAM (Science, Technology, Engineering, Arts, Mathematics) 
paradigm that emphasizes integrative and creative problem-solving. However, 
evaluating innovation ability is challenging due to its multidimensionality, vagueness, 
and subjectivity. This paper introduces a novel Neutrosophic SuperHyper 
Pentapartitioned Process Model (NSPPM) designed to rigorously capture uncertainty, 
contradiction, and incompleteness in students’ innovation assessment. Building on the 
formalism of Single-Valued Pentapartitioned Neutrosophic Sets (SVPNS), the model 
decomposes student performance into five dimensions: truth (T), contradiction (C), 
ignorance (G), uncertainty (U), and falsehood (F). These are then aggregated across multi
level tasks using a superhyperstructure composition that ensures closure, monotonicity, 
and idempotence. Decision-making is achieved via a dominance relation that compares 
students across dimensions, preserving the neutrosophic nature of the evaluation without 
collapsing it into scalar indices. To illustrate, synthetic case studies simulate student 
performance under STEAM tasks in engineering and arts, demonstrating how NSPPM 
identifies non-dominated students and reveals nuanced patterns of innovation capacity. 
The results highlight both the theoretical novelty of pentapartitioned neutrosophic 
superhyper modeling and its practical utility in educational evaluation. 

DOI: 10.5281/zenodo.16934640