Anti-Fuzzy Hypergraphs and Superhypergraphs: Max-Oriented Uncertainty Models for Higher-Order and Hierarchical Networks

Takaaki Fujita, Independent Researcher, Tokyo, JapanFollow
Ajoy Kanti Das, Associate Professor, Department of Mathematics, Tripura University, Agartala-799022, Tripura, IndiaFollow
Suman Das, Assistant Professor Grade II (Mathematics), Department of Education, National Institute of Technology Calicut, Kozhikode-673601, Kerala, IndiaFollow
Sankar Prasad Mondal, Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, Haringhata-741249, West Bengal, IndiaFollow

ORCID

Takaaki Fujita: https://orcid.org/0000-0002-9380-386X

Ajoy Kanti Das: https://orcid.org/0000-0002-9326-1677

Suman Das: https://orcid.org/0000-0001-5682-9334

Sankar Prasad Mondal: https://orcid.org/0000-0003-4690-2598

Keywords

Anti-fuzzy graph, Anti-fuzzy hypergraph, Anti-fuzzy SuperHyperGraph, Fuzzy hypergraph, Fuzzy SuperHyperGraph, SuperHyperGraph

Article Type

Original Article

Abstract

Hypergraphs extend classical graphs by allowing hyperedges to connect more than two vertices, while superhypergraphs further generalize this framework through iterated powerset constructions that capture hierarchical and nested incidence structures. Within fuzzy graph theory, anti-fuzzy graphs provide max-oriented uncertainty models in which each edge grade is at least the maximum grade of its incident vertices. However, corresponding max-oriented frameworks for hypergraphs and superhypergraphs have not been systematically developed. To address this gap, we introduce anti-fuzzy hypergraphs and anti-fuzzy superhypergraphs, formulate their mathematical definitions, and establish basic well-definedness and canonical representation results. These models provide a unified foundation for max-based uncertainty modeling in higher-order and hierarchical network structures.

How to Cite

Fujita, Takaaki; Das, Ajoy Kanti; Das, Suman; and Mondal, Sankar Prasad (2026) "Anti-Fuzzy Hypergraphs and Superhypergraphs: Max-Oriented Uncertainty Models for Higher-Order and Hierarchical Networks," Sustainable Machine Intelligence Journal: Vol. 14: Iss. 3, Article 5.
DOI: https://doi.org/10.63689/3005-3617.1095