Sustainable Framework for Performance-Based Learning Assessment under Uncertainty: Computational Modeling

Mona Gharib, Department of Mathematics, Faculty of Science, Zagazig University, 44519 Zagazig, EgyptFollow
Muhammad Imran, Department of Economics, Management and Business Law, Universita Degli Studi Di Bari Aldo Moro, Bari, ItalyFollow
Zaka Ur Rehman, Department of International Business Management, Ulster University, B5 4UA Birmingham, UKFollow

ORCID

Mona Gharib: https://orcid.org/0009-0006-7367-4307

Muhammad Imran: https://orcid.org/0009-0002-7491-7498

Zaka Ur Rehman: https://orcid.org/0009-0003-6929-6655

Keywords

Neutrosophic Logic, Functional Analysis, Performing Arts Evaluation, Computational Modeling, Intelligent Assessment

Article Type

Original Article

Abstract

Evaluating performance-based learning, such as dance or performing arts education, poses significant computational challenges due to uncertainty, subjectivity, and heterogeneous evaluation data. Conventional scoring models fail to capture the coexistence of quantitative indicators (timing, attendance) and qualitative judgments (artistry, expressiveness).

This study introduces a computational neutrosophic functional framework that models ambiguity using set-valued, indeterminate representations within a rigorous analytic structure. We construct a neutrosophic function space CN(X) and a Hilbert C*-module HN for integrating evaluator signals through algebraic fusion. A strongly continuous neutrosophic operator semigroup (T(t)) is developed to model temporal learning and decay, while a neutrosophic Fourier–Stieltjes expansion captures periodic instructional effects. The framework’s theoretical core—the Neutrosophic Banach–Stone Principle—links structure-preserving isometries to homeomorphisms of attribute spaces. A computational case study on college dance evaluation demonstrates the system’s capacity to unify uncertain, multi-source data in a stable analytic environment. The approach offers a foundation for intelligent assessment systems in performing arts and related learning domains.

How to Cite

Gharib, Mona; Imran, Muhammad; and Rehman, Zaka Ur (2025) "Sustainable Framework for Performance-Based Learning Assessment under Uncertainty: Computational Modeling," Sustainable Machine Intelligence Journal: Vol. 13: Iss. 1, Article 4.
DOI: https://doi.org/10.63689/3005-3617.1075