Fuzzy and Neutrosophic Directed Superhypergraphs: Definitions, Properties, and Illustrative Real-World Applications in Decision-Making.

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Title:	Fuzzy and Neutrosophic Directed Superhypergraphs: Definitions, Properties, and Illustrative Real-World Applications in Decision-Making.
Authors:	Fujita, Takaaki Takaaki.fujita060@gmail.com, Smarandache, Florentin¹ fsmarandache@gmail.com
Source:	IAENG International Journal of Applied Mathematics. May2026, Vol. 56 Issue 5, p1681-1701. 21p.
Subjects:	Hypergraphs, Fuzzy sets, Mathematical models, Neutrosophic logic, Graph theory, Decision support systems
Abstract:	Graph theory examines mathematical structures composed of vertices and edges to model relationships and connectivity. Hypergraphs generalize classical graphs by permitting hyperedges that connect more than two vertices simultaneously. Hypergraphs have been further extended to directed hypergraphs. Superhypergraphs build on this idea by introducing iterated powerset layers, enabling hierarchical and selfreferential connections among hyperedges. Superhypergraphs have likewise been extended to directed superhypergraphs. These graph concepts have been enriched by frameworks such as fuzzy sets, soft sets, intuitionistic fuzzy sets, neutrosophic sets, hesitant fuzzy sets, and plithogenic sets. In this paper, we introduce and explore the concepts of Fuzzy Directed Superhypergraphs and Neutrosophic Directed Superhypergraphs. To enhance understanding and support future applications, we also provide concrete examples involving real-world decisionmaking scenarios. We expect that these contributions will stimulate further research in the areas of superhypergraphs, hypergraphs, fuzzy graphs, neutrosophic graphs, and other related mathematical frameworks. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

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Abstract:	Graph theory examines mathematical structures composed of vertices and edges to model relationships and connectivity. Hypergraphs generalize classical graphs by permitting hyperedges that connect more than two vertices simultaneously. Hypergraphs have been further extended to directed hypergraphs. Superhypergraphs build on this idea by introducing iterated powerset layers, enabling hierarchical and selfreferential connections among hyperedges. Superhypergraphs have likewise been extended to directed superhypergraphs. These graph concepts have been enriched by frameworks such as fuzzy sets, soft sets, intuitionistic fuzzy sets, neutrosophic sets, hesitant fuzzy sets, and plithogenic sets. In this paper, we introduce and explore the concepts of Fuzzy Directed Superhypergraphs and Neutrosophic Directed Superhypergraphs. To enhance understanding and support future applications, we also provide concrete examples involving real-world decisionmaking scenarios. We expect that these contributions will stimulate further research in the areas of superhypergraphs, hypergraphs, fuzzy graphs, neutrosophic graphs, and other related mathematical frameworks. [ABSTRACT FROM AUTHOR]
ISSN:	19929978