Neutrosophic Bishop Graphs: Geometric and Computational Reasoning Under Uncertainty

Neutrosophic Bishop Graphs (NBGs), a graph-theoretic framework for making decisions in situations with
ambiguity, inconsistency and multi-criteria dependence are presented in this study. Neutrosophic Bishop Graphs
(NBGs), model inference as path-based propagation of truth, indeterminacy and falsehood, building on
Neutrosophic logic and a geometric constraint inspired by diagonal movement in chess. Formal definitions,
dominance-based inference, aggregate semantics, a worked diagnostic case and comprehensive theoretical analysis
are all provided. Specifically, we prove NP-completeness of precise inference, establish monotonicity properties
and derive fixed-parameter tractability results and ɛ-approximation guarantees. The framework provides a
computationally valid and accessible substitute for fuzzy and probabilistic decision models.