A Theoretical Investigation Based on the Rough Approximations of Hypergraphs
Rough sets are a key tool to model uncertainty and vagueness using upper and lower approximations without predefined functions and additional suppositions. Rough graphs cannot be studied more effectively when the inexact and approximate relations among more than two objects are to be discussed. In t...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/1540004 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832549565725671424 |
|---|---|
| author | Musavarah Sarwar |
| author_facet | Musavarah Sarwar |
| author_sort | Musavarah Sarwar |
| collection | DOAJ |
| description | Rough sets are a key tool to model uncertainty and vagueness using upper and lower approximations without predefined functions and additional suppositions. Rough graphs cannot be studied more effectively when the inexact and approximate relations among more than two objects are to be discussed. In this research paper, the notion of a rough set is applied to hypergraphs to introduce the novel concept of rough hypergraphs based on rough relations. The notions of isomorphism, conformality, linearity, duality, associativity, commutativity, distributivity, Helly property, and intersecting families are illustrated in rough hypergraphs. The formulae of 2-section, L2-section, covering, coloring, rank, and antirank are established for certain types of rough hypergraphs. The relations among certain types of products of rough hypergraphs are studied in detail. |
| format | Article |
| id | doaj-art-25d23f3b1a9b4caf9bfb52419c6cfb6b |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-25d23f3b1a9b4caf9bfb52419c6cfb6b2025-02-03T06:10:55ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/1540004A Theoretical Investigation Based on the Rough Approximations of HypergraphsMusavarah Sarwar0Department of MathematicsRough sets are a key tool to model uncertainty and vagueness using upper and lower approximations without predefined functions and additional suppositions. Rough graphs cannot be studied more effectively when the inexact and approximate relations among more than two objects are to be discussed. In this research paper, the notion of a rough set is applied to hypergraphs to introduce the novel concept of rough hypergraphs based on rough relations. The notions of isomorphism, conformality, linearity, duality, associativity, commutativity, distributivity, Helly property, and intersecting families are illustrated in rough hypergraphs. The formulae of 2-section, L2-section, covering, coloring, rank, and antirank are established for certain types of rough hypergraphs. The relations among certain types of products of rough hypergraphs are studied in detail.http://dx.doi.org/10.1155/2022/1540004 |
| spellingShingle | Musavarah Sarwar A Theoretical Investigation Based on the Rough Approximations of Hypergraphs Journal of Mathematics |
| title | A Theoretical Investigation Based on the Rough Approximations of Hypergraphs |
| title_full | A Theoretical Investigation Based on the Rough Approximations of Hypergraphs |
| title_fullStr | A Theoretical Investigation Based on the Rough Approximations of Hypergraphs |
| title_full_unstemmed | A Theoretical Investigation Based on the Rough Approximations of Hypergraphs |
| title_short | A Theoretical Investigation Based on the Rough Approximations of Hypergraphs |
| title_sort | theoretical investigation based on the rough approximations of hypergraphs |
| url | http://dx.doi.org/10.1155/2022/1540004 |
| work_keys_str_mv | AT musavarahsarwar atheoreticalinvestigationbasedontheroughapproximationsofhypergraphs AT musavarahsarwar theoreticalinvestigationbasedontheroughapproximationsofhypergraphs |