Matroidal and Lattices Structures of Rough Sets and Some of Their Topological Characterizations

Authors

Abd El Fattah A. El Atik, Mathematics Department, Faculty of Science, Tanta University, 31511 Tanta, EgyptFollow
Manal E. Ali, Department of Physics and Engineering Mathematics, Faculty of Engineering, Kafrelsheikh University, 33516, Kafrelsheikh, EgyptFollow

Abstract

Matroids, rough set theory and lattices are efficient tools of knowledge discovery. Lattices and matroids are studied on preapproximations spaces. Li et al. proved that a lattice is Boolean if it is clopen set lattice for matroids. In our study, a lattice is Boolean if it is closed for matroids. Moreover, a topological lattice is discussed using its matroidal structure. Atoms in a complete atomic Boolean lattice are completely determined through its topological structure. Finally, a necessary and sufficient condition for a predefinable set is proved in preapproximation spaces. The value k for a predefinable set in lattice of matroidal closed sets is determined.

Recommended Citation

El Fattah A. El Atik, Abd and E. Ali, Manal (2022) "Matroidal and Lattices Structures of Rough Sets and Some of Their Topological Characterizations," Information Sciences Letters: Vol. 11 : Iss. 2 , PP -.
Available at: https://digitalcommons.aaru.edu.jo/isl/vol11/iss2/35