A neutrosophic explainable AI framework for modeling uncertainty in immersive stereotactic neurosurgical simulation

The integration of Artificial Intelligence (AI) and Virtual Reality (VR) has transformed medical education; however, performance assessment in high-stakes fields such as stereotactic neurosurgery remains largely dependent on binary or threshold-based metrics. In procedures such as deep brain stimulation (DBS), where safety margins are below 2 mm, these approaches fail to capture indeterminate behaviors, including hesitation, micro-instability, and unstable trajectories, potentially leading to false-positive competence classifications. This study introduces a Neutrosophic Explainable AI (N-XAI) framework that models surgical performance through three independent dimensions: truth (competence), Indeterminacy (instability/ambiguity), and Falsity (error). Performance is represented in a two-dimensional precision-stability space and quantified using single-valued neutrosophic sets (SVNS). For theoretical validation, a synthetic dataset comprising 60 simulated surgical attempts distributed across three skill groups (expert, indeterminate, and novice) was generated. Neutrosophic competence scores were computed and analyzed using non-parametric statistical tests. The framework successfully differentiated the three groups and identified indeterminate, high-risk cases that achieved acceptable spatial accuracy but exhibited significant instability-patterns that conventional metrics fail to detect. The proposed N-XAI framework provides a mathematically grounded and interpretable approach for modeling uncertainty in immersive neurosurgical simulation. By explicitly accounting for indeterminacy, it enhances the diagnostic value of VR-based training systems and lays the groundwork for future validation in live stereotactic simulation environments.