Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 10.54216/PAMDA https://www.americaspg.com/journals/show/3987 2022 2022 Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan Takaaki Takaaki Department of Mathematics, University of Management and Technology, Lahore, 54000, Pakistan Atiqe Ur Rahman Department of Information Technology, Management Technical College, Southern Technical University, Basrah, 61004, Iraq Arkan A. Ghaib Department of Mathematics, Yarmouk University, Irbid, Jordan Talal Ali Al Al-Hawary Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan 29050, KPK, Pakistan Arif Mehmood Khattak 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 2025 12 31 10.54216/PAMDA.050102 https://www.americaspg.com/articleinfo/34/show/3987