Advancing Soft Graph Theory: Formalization of HyperSoft and SuperHyperSoft HyperGraphs and SuperHyperGraphs
Year: 2025
Type: preprint
Abstract: Graph theory investigates structures composed of nodes and edges to model relationships or connections. A hypergraph generalizes the concept of a traditional graph by allowing edges-called hyperedges-to connect more than two vertices simultaneously [1]. A superhypergraph further extends this concept by incorporating recursively defined powerset layers, enabling hierarchical and self-referential relationships among hyperedges [2]. A soft graph represents parameterized graph structures in which each parameter defines a subgraph over a fixed vertex and edge set. Furthermore, generalized notions of soft graphs, such as the HyperSoft Graph and Super-HyperSoft Graph, are also known and have been studied in applications including decision-making. However, concepts corresponding to HyperSoft Graph and SuperHyperSoft Graph in the context of superhypergraphs have not yet been extensively explored. To bridge this gap, this paper introduces the notions of HyperSoft HyperGraph, SuperHyperSoft HyperGraph, SuperHyperSoft SuperHyperGraph, and SuperHyperSoft Hyper-Graph. These frameworks are expected to enable the generalization of more hierarchical and complex concepts found in the real world.
Author: Takaaki Fujita
Language: English
Topic: Fuzzy and Soft Set Theory
Field: Decision Sciences
Domain: Social Sciences
Open Access status: gold
OpenAlex ID: W4413638606