Fuzzy, Neutrosophic, and Uncertain Graph Theory: Properties and Applications
Summary
This book presents a comprehensive survey of graph theory under uncertainty, covering fuzzy, neutrosophic, and uncertain graph models, their properties, extensions, and applications in decision-making, graph neural networks, and knowledge graphs.
View Cached Full Text
Cached at: 05/26/26, 09:00 AM
# Fuzzy, Neutrosophic, and Uncertain Graph Theory: Properties and Applications Source: [https://arxiv.org/abs/2605.23936](https://arxiv.org/abs/2605.23936) [View PDF](https://arxiv.org/pdf/2605.23936) > Abstract:This book presents a comprehensive and systematic survey of graph theory under uncertainty, with particular emphasis on the unifying role of the uncertain graph framework\. It reviews fundamental concepts, structural properties, graph classes, and graph parameters within fuzzy, neutrosophic, and related models, while also introducing a wide range of extensions such as uncertain digraphs, hypergraphs, superhypergraphs, and dynamic graphs\. In addition to theoretical developments, the book explores practical applications, including uncertain molecular graphs, decision\-making systems, graph neural networks, knowledge graphs, and cognitive maps\. By organizing diverse uncertainty\-aware graph models within a common perspective, this work provides a coherent framework for understanding their relationships, capabilities, and applications in complex systems\. ## Submission history From: Takaaki Fujita \[[view email](https://arxiv.org/show-email/c7c4d9c7/2605.23936)\] **\[v1\]**Sat, 25 Apr 2026 07:35:19 UTC \(2,032 KB\)
Similar Articles
Scalable Uncertainty Reasoning in Knowledge Graphs
This thesis proposes a modular framework for scalable uncertainty reasoning in knowledge graphs, addressing imprecise attribute values, probabilistic triple existence, and incomplete schema through tailored algebraic, logical, and geometric techniques.
Breaking the Chains of Probability: Neutrosophic Logic as a New Framework for Epistemic Uncertainty in Large Language Models
This paper investigates Neutrosophic Logic as a framework for modeling epistemic states in Large Language Models, demonstrating that it can capture 'hyper-truth' states beyond traditional probability constraints, leading to more transparent and ethically aware AI systems.
Beyond Semantic Equivalence: Logical Graphs for LLM Uncertainty Quantification
This paper proposes Logical Graph Uncertainty (LGU), a framework that models implication and incompatibility among answers to improve uncertainty estimation in LLMs, outperforming semantic entropy baselines by up to 7.1% AUROC and 3.5% AUARC across benchmarks.
Are you sure? A Comprehensive and Comprehensible Survey of Uncertainty Quantification in Symbolic Regression
A comprehensive survey on uncertainty quantification in symbolic regression, reviewing frequentist, Bayesian, and model selection approaches to address the lack of reliability support in real-world decision processes.
Knowledge Graphs Meet Graph Neural Networks: A Comprehensive Survey
This comprehensive survey systematically reviews graph neural network-based methods across the entire knowledge graph pipeline, proposing a novel two-level taxonomy and discussing challenges and future research directions.