A Short Note on Interval-Valued Bipolar Fuzzy SuperHyperGraphs
Takaaki Fujita1,∗, Ajoy Kanti Das2, Sankar Prasad Mondal3, Suman Das4
1Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan
2Associate Professor, Department of Mathematics, Tripura University, Agartala-799022, Tripura, India
3Department of Applied Mathematics, Maulana Abul Kalam Azad University of Technology, West Bengal,
Haringhata-741249, West Bengal, India
4Assistant Professor (Mathematics), Department of Education (ITEP), NIT Agartala, Jirania, 799046,
Tripura, India
Emails: Takaaki.fujita060@gmail.com; ajoykantidas@gmail.com; sankar.mondal02@gmail.com;
dr.sumandas1995@gmail.com
Abstract
Hypergraphs extend classical graphs by allowing hyperedges to connect arbitrary nonempty subsets of ver-
tices, thereby capturing higher-order, group-level interactions. Superhypergraphs further broaden this setting
by iterating the powerset construction, which yields layered supervertices and supports multi-level relational
structure. An interval-valued bipolar fuzzy graph assigns positive and negative membership intervals to ver-
tices and edges while satisfying bipolar consistency constraints. In this paper, we extend interval-valued
bipolar fuzzy graphs to the settings of hypergraphs and superhypergraphs.
Keywords: SuperHyperGraph; HyperGraph; Fuzzy SuperHyperGraph; Interval-valued bipolar fuzzy graph