A Neutrosophic Homological-Gröbner Framework for AI-Driven media Education Evaluation

Mona Gharib, Department of Mathematics, Faculty of Science, Zagazig University, 44519 Zagazig, EgyptFollow
Hafiz Muhammad Athar Farid, Department of Computer Science, University of Huddersfield, Huddersfield, UKFollow
José M. Merigó, School of Computer Science, Faculty of Engineering and Information Technology, University of Technology Sydney, 81 Broadway, Ultimo 2007, NSW, AustraliaFollow
Muhammad Riaz, Institute of Mathematics, University of the Punjab, Lahore PakistanFollow

ORCID

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

Hafiz Muhammad Athar Farid: https://orcid.org/0000-0002-8318-0750

Jos\\'e M. Merig\\'o: https://orcid.org/0000-0002-4672-6961

Muhammad Riaz: https://orcid.org/0000-0001-8115-9168

Keywords

Neutrosophic sets, Homological algebra, Betti indices, Chain complex, Gröbner bases, multi-criteria decision making, uncertainty modeling, intelligent teaching quality, Journalism and communication, AI driven media education

Article Type

Original Article

Abstract

The integration of artificial intelligence (AI) with media technologies has transformed teaching in Journalism and Communication, introducing new challenges for quality evaluation. Traditional assessment methods fail to capture the uncertainty, inconsistency, and incompleteness inherent in modern educational data. This paper proposes a Neutrosophic Homological–Gröbner Framework, which unifies three perspectives: neutrosophic sets to encode uncertain evidence, homological algebra to analyze structural coherence, and Gröbner bases to systematically simplify interdependent evaluation rules.

Within this framework, diverse evidence is encoded into neutrosophic triplets, daggregate into course-level indicators, and organized into neutrosophic chain complexes, where Betti indices reveal coherence and fragmentation. Educational policies are formulated as neutrosophic polynomial constraints, and Gröbner reduction produces a canonical rubric ranked by evidential support. A case study in Journalism and Communication demonstrates that the method is stable under perturbations and yields interpretable, contradiction-minimized guidelines. The results confirm that directly modeling uncertainty enables more robust and transparent evaluation in AI-driven media education.

How to Cite

Gharib, Mona; Farid, Hafiz Muhammad Athar; Merigó, José M.; and Riaz, Muhammad (2026) "A Neutrosophic Homological-Gröbner Framework for AI-Driven media Education Evaluation," Sustainable Machine Intelligence Journal: Vol. 14: Iss. 1, Article 1.
DOI: https://doi.org/10.63689/3005-3617.1078