Mathematics and Computational Sciences

Algebraic structures and lattice properties of hypergraph Pre-Rough sets‎

Document Type : Original Article

Authors

Ganesan Gomathi 1
Peer Mohaideen Miya Fathima Benazir 2
Shriram Kalathian 3
Subbaraj Marichamy 4

1 Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India.

2 Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai, Tamil Nadu, India

3 Department of Mathematics, St. Joseph's Institute of Technology, Old Mahabalipuram Road, Chennai, 600119, Tamil Nadu, India.

4 Department of Mathematics, Chennai Institute of Technology, Chennai,Tamil Nadu, India

https://doi.org/10.30511/mcs.2025.2074948.1504
Abstract
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.

Keywords

Rough sets
Soft sets
Covering-based soft sets
Hypergraph rough sets

Subjects

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Mathematics and Computational Sciences
Volume 6, Issue 4
Autumn 2025
Pages 20-32

  • Receive Date 17 October 2025
  • Revise Date 18 November 2025
  • Accept Date 26 November 2025

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