Algebraic structures and lattice properties of hypergraph Pre-Rough sets

The study introduces and examines the concept of hypergraph pre-rough sets, which are developed by combining minimum soft descriptions with hypergraph structures. It defines this set's theoretical foundation and emphasises its essential algebraic characteristics. The study also indicates that the sum of all hypergraph pre-rough sets forms a lattice in a canonical ordering. By integrating basic soft descriptions to hypergraph-based approximations, the proposed framework effectively represents higher-order relational uncertainty. The results improve the algebraic structure of rough set theory and provide a foundation for further research in complex network analysis, multi-parameter decision-making, and hypergraph-based uncertainty modelling.