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

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.