Neutrosophic Graded Jordan–Bialgebra Framework for AI-Driven Analysis

Authors

Mona Gharib, Department of Mathematics, Faculty of Science, Zagazig University, 44519 Zagazig, EgyptFollow
Rana Muhammad Zulqarnain, Department of Mathematics, Zhejiang Normal University, Zhejiang, ChinaFollow
Xiao Long Xin, School of Mathematics, Northwest University, Xi’an, ChinaFollow
Muhammad Gulistan, Department of Electrical and Computer Engineering, University of Alberta, CanadaFollow
Muhammad Abid, Department of Mathematics, North Carolina State University, Raleigh, 27695, NC, United StatesFollow

ORCID

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

Rana Muhammad Zulqarnain: https://orcid.org/0000-0002-2656-8679

Xiao Long Xin: https://orcid.org/0000-0002-8495-7322

Muhammad Gulistan: https://orcid.org/0000-0002-6438-1047

Muhammad Abid: https://orcid.org/0009-0006-8619-6666

Article Type

Research Article

Abstract

Modern Artificial Intelligence (AI) systems face significant challenges in processing and analyzing datasets characterized by high degrees of uncertainty, ambiguity, and indeterminacy, which are prevalent features in complex real-world scenarios. To address this limitation, this study introduces a novel neutrosophic graded Jordan–bialgebra framework. This framework strategically integrates the inherent structural properties of Jordan–Bialgebras with the advanced capability of Neutrosophic Graded Structures to simultaneously model degrees of truth, indeterminacy, and falsehood. The primary objective of this study is to establish a rigorous algebraic foundation that enables AI models to perform a more robust and comprehensive analysis of data containing incomplete or contradictory information.

A case study on university physics teaching supported by AI-driven learning data demonstrates the framework’s ability to identify strong synergies, detect hidden conflicts, and perform sensitivity analysis under high indeterminacy. The results highlight the robustness of neutrosophic algebraic structures in handling educational uncertainty and provide a pathway toward more reliable evaluations of teaching effectiveness in AI-enhanced environments.

Keywords

Neutrosophic algebra, Graded Jordan–bialgebra, AI-Driven analysis, Uncertainty modeling, Educational data analysis

How to Cite

Gharib, Mona; Zulqarnain, Rana Muhammad; Xin, Xiao Long; Gulistan, Muhammad; and Abid, Muhammad (2025) "Neutrosophic Graded Jordan–Bialgebra Framework for AI-Driven Analysis," Neutrosophic Systems with Applications: Vol. 25: Iss. 11, Article 1. DOI: https://doi.org/10.63689/2993-7159.1305