Neutrosophic Graded Jordan–Bialgebra Framework for AI-Driven Analysis

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.