HyperFuzzy Graph and Hyperfuzzy HyperGraph

Takaaki Fujita1,∗ , Prem Kumar Singh2

1Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan

2Department of Computer Science and Engineering, Gandhi Institute of Technology and Management,

Visakhapatnam, Andhra Pradesh 530045, India

Emails: takaaki.fujita060@gmail.com; premsingh.csjm@gmail.com

Abstract

Fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, plithogenic sets, and other uncertainty-handling frame-

works are the subject of intensive daily research. Analogous investigations have been pursued in the contexts

of graphs, hypergraphs, and superhypergraphs. In this paper, we introduce new definitions of the hyperfuzzy

hypergraph and superhyperfuzzy hypergraph, which extend the notion of the fuzzy hypergraph. We also revisit

and refine the concepts of the hyperfuzzy graph and the superhyperfuzzy graph.

Keywords: Hyperfuzzy set; Fuzzy set; SuperHyperfuzzy Set; Hyperfuzzy graph; Fuzzy graph; SuperHyper-

fuzzy graph