Fuzzy, Neutrosophic, and Uncertain Graph Theory (3): A Survey and Unified Framework for Uncertain Intersection Graphs

This book presents a comprehensive treatment of intersection graph theory within modern uncertainty-aware mathematical frameworks. Beginning with the foundations of classical graph theory and the major families of intersection graphs—including interval, disk, circle, circular-arc, ray, string, grid, and related geometric graph classes—it develops a unified perspective that integrates fuzzy, intuitionistic fuzzy, neutrosophic, plithogenic, and general uncertain graph models into a common theoretical framework. The volume surveys existing literature while introducing several original contributions, including a general definition of uncertain graphs based on arbitrary uncertainty models, a unified theory of uncertain intersection graphs, and corresponding geometric subclasses such as uncertain unit square graphs, uncertain circle graphs, uncertain ray graphs, uncertain string graphs, and uncertain grid intersection graphs. The book further proposes the novel concepts of Multi-Intersection Graphs, Quasi-Intersection Graphs, Metric Quasi-Intersection Graphs, and Multi-Quasi-Intersection Graphs, together with their fundamental properties and well-definedness results. By combining a broad survey with new theoretical developments, the work establishes a coherent foundation for modeling complex geometric and relational structures under uncertainty. It is intended as a reference for researchers and graduate students working in graph theory, uncertainty modeling, fuzzy systems, neutrosophic mathematics, artificial intelligence, computational geometry, and related interdisciplinary fields, while also providing a basis for future algorithmic, computational, and applied investigations.