aspg-34-3987-1791482222 20261008175702 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 2025 5 1 Takaaki Fujita Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan Atiqe Ur Rahman Department of Mathematics, University of Management and Technology, Lahore, 54000, Pakistan Arkan A. Ghaib Department of Information Technology, Management Technical College, Southern Technical University, Basrah, 61004, Iraq Talal Ali Al-Hawary Department of Mathematics, Yarmouk University, Irbid, Jordan Arif Mehmood Khattak Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, KPK, Pakistan In graph theory, a hypergraph generalizes a classical graph by allowing each hyperedge to join any number of vertices, thereby modeling relationships beyond simple pairwise connections.[1] A superhypergraph takes this further by applying recursive powerset constructions to its hyperedge set, creating hierarchical and self-referential network layers.[2] A soft graph defines a family of subgraphs parameterized over a fixed universe of vertices and edges, while a rough graph uses lower and upper approximations to capture uncertainty in graph structure. In this paper, we revisit Soft SuperHypergraphs and Rough SuperHypergraphs—originally introduced in [3]—which integrate the flexibility of soft and rough graph frameworks with the layered com- plexity of superhypergraphs. We provide precise definitions, illustrative examples, and a detailed analysis of their fundamental properties, demonstrating their potential for modeling hierarchical and uncertain network systems. 2025 08 19 3987 https://creativecommons.org/licenses/by/4.0/ 10.54216/PAMDA.050102 https://www.americaspg.com/journal/34/article/3987 https://www.americaspg.com/storage/articles/manuscripts/01KZQ540JV0DC7RC9303NNDNHM.pdf