Open AccessRough topological structure based on reflexivity with some applications
Author(s) -
E. A. Abo-Tabl,
Mostafa K. El-Bably
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022553
Subject(s) - rough set , topological space , closure (psychology) , mathematics , relation (database) , reflexivity , representation (politics) , space (punctuation) , topology (electrical circuits) , connected space , dengue fever , pure mathematics , set (abstract data type) , topological vector space , computer science , combinatorics , medicine , artificial intelligence , data mining , sociology , social science , immunology , politics , economics , political science , law , market economy , programming language , operating system
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.