Modeling Reliability, Ambiguity, and Risk in Information Technology Management Using Quaternion Fuzzy and Quaternion Neutrosophic Graphs

Reliability assessment, ambiguity handling, and risk management are fundamental challenges in contemporary information technology management, where decision-making often relies on incomplete, uncertain, and heterogeneous information. Graph-based uncertainty models, including fuzzy and neutrosophic graphs, provide useful tools for representing dependencies and interactions among system components. However, complex IT environments frequently require richer representations capable of capturing multiple dimensions of uncertainty within a unified framework. To address this challenge, we introduce quaternion-based graph models for uncertainty representation in information technology management. Specifically, we develop quaternion fuzzy graphs, in which vertices and edges are labeled by elements of the quaternion unit ball and edge labels satisfy a norm-bounded incidence condition induced by their endpoints. We further propose quaternion neutrosophic graphs, where truth, indeterminacy, and falsity information are encoded through pure-quaternion components, providing a compact and expressive representation of uncertain relationships. We establish the fundamental properties of the proposed models and show that they preserve the corresponding quaternion fuzzy and quaternion neutrosophic set structures. Moreover, classical fuzzy graphs and single-valued neutrosophic graphs are recovered as special cases through canonical embeddings and componentwise reductions. The proposed framework offers a unified approach for modeling reliability, ambiguity, dependency strength, and risk in interconnected IT systems. Illustrative applications in IT Service Management and IT Project Management demonstrate its potential for representing complex dependencies and supporting uncertainty-aware analysis and decision-making in information technology management environments.