Fuzzy, Neutrosophic, and Uncertain Graph Theory: Properties and Applications

arXiv cs.AI Papers

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.

arXiv:2605.23936v1 Announce Type: new 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.
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# Fuzzy, Neutrosophic, and Uncertain Graph Theory: Properties and Applications
Source: [https://arxiv.org/abs/2605.23936](https://arxiv.org/abs/2605.23936)
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> 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 \(2,032 KB\)

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