A novel pessimistic multigranulation roughness by soft relations over dual universe

Jamalud Din; Muhammad Shabir; Samir Brahim Belhaouari; Jamalud Din; Muhammad Shabir; Samir Brahim Belhaouari

doi:10.3934/math.2023397

AIMS Mathematics

2023, Volume 8, Issue 4: 7881-7898. doi: 10.3934/math.2023397

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A novel pessimistic multigranulation roughness by soft relations over dual universe

1.
Department of Mathematics, Quaid-I-Azam University Islamabad, 44230, Pakistan
2.
Division of Information and Computing Technology, College of Science and Engineering, Hamad Bin Khalifa University, Doha, Qatar

Received: 12 September 2022 Revised: 31 December 2022 Accepted: 10 January 2023 Published: 31 January 2023
MSC : 03B52, 68T27

A multigranulation rough set over two universes delivers a unique perspective on the combination of multigranulation information. This paper presents the pessimistic multignualtion rough set over dual universes based on soft binary relations. Firstly, a new pessimistic multigranualtion rough set over dual universes based on two soft binary relations has been developed, and their properties are derived. Then we extend this idea and present pessimistic multigranulation roughness over dual universes based on the finite number of soft binary relations. Finally, we present an example to illustrate our proposed multigranualtion rough set model.
- rough set,
- soft set,
- multigranulation rough set,
- soft relation and approximation by soft binary relation
Citation: Jamalud Din, Muhammad Shabir, Samir Brahim Belhaouari. A novel pessimistic multigranulation roughness by soft relations over dual universe[J]. AIMS Mathematics, 2023, 8(4): 7881-7898. doi: 10.3934/math.2023397

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Abstract

A multigranulation rough set over two universes delivers a unique perspective on the combination of multigranulation information. This paper presents the pessimistic multignualtion rough set over dual universes based on soft binary relations. Firstly, a new pessimistic multigranualtion rough set over dual universes based on two soft binary relations has been developed, and their properties are derived. Then we extend this idea and present pessimistic multigranulation roughness over dual universes based on the finite number of soft binary relations. Finally, we present an example to illustrate our proposed multigranualtion rough set model.

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