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AIMS Mathematics

2022, Volume 7, Issue 6: 9911-9925. doi: 10.3934/math.2022553
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Research article

Rough topological structure based on reflexivity with some applications

  • 1.
    Mathematics Department, Faculty of Science, Assiut University, Assiut, Egypt
  • 2.
    Mathematics Department, College of Science and Arts, Methnab, Qassim University, Buridah, Saudi Arabia
  • 3.
    Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt
  • Received: 21 November 2021 Revised: 05 March 2022 Accepted: 07 March 2022 Published: 18 March 2022

  • MSC : 54A05, 54A10, 03E20

  • Recently, topological structures have emerged as one of the most popular rough sets (RS) research topics. It can be stated that it is a fundamental and significant subject in the theory of RS. This study introduces a debate about the structure of rough topological space based on the reflexive relation. To create the rough topological space, we use the representation of RS. We also look at the relationships between approximation operators, closure operators, and interior operators. Also, the relationship between topological space in the universe that is not limited or restricted to be ended, and RS induced by reflexive relations is investigated. Furthermore, we define the relationships between the set of all topologies that satisfy the requirement of compactness $ C_{2} $ and the set of all reflexive relations. Finally, we present a medical application that addresses the issue of dengue fever. The proposed structures are used to determine the impact factors for identifying dengue fever.

    Citation: El-Sayed A. Abo-Tabl, Mostafa K. El-Bably. Rough topological structure based on reflexivity with some applications[J]. AIMS Mathematics, 2022, 7(6): 9911-9925. doi: 10.3934/math.2022553

    Related Papers:

  • Recently, topological structures have emerged as one of the most popular rough sets (RS) research topics. It can be stated that it is a fundamental and significant subject in the theory of RS. This study introduces a debate about the structure of rough topological space based on the reflexive relation. To create the rough topological space, we use the representation of RS. We also look at the relationships between approximation operators, closure operators, and interior operators. Also, the relationship between topological space in the universe that is not limited or restricted to be ended, and RS induced by reflexive relations is investigated. Furthermore, we define the relationships between the set of all topologies that satisfy the requirement of compactness $ C_{2} $ and the set of all reflexive relations. Finally, we present a medical application that addresses the issue of dengue fever. The proposed structures are used to determine the impact factors for identifying dengue fever.


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