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Matroidal and Lattices Structures of Rough Sets and Some of Their Topological Characterizations |
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PP: 331-341 |
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doi:10.18576/isl/110204
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Author(s) |
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Abd El Fattah A. El Atik,
Manal E. Ali,
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Abstract |
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| 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. |
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