The Lattice of Rough Subsets of a Rough Set. The Category of Rough Sets
Copyright policy )The Lattice of Rough Subsets of a Rough Set. The Category of Rough Sets
The paper deals with algebraic structures related to rough sets, introduced by Pawlak in 1982. It is proved that the lattice of all rough subsets of a given rough set is a complete Heyting algebra. Necessary and sufficient conditions for the above lattice to be a Boolean algebra are presented. The relationships between rough sets and Heyting algebras (valued sets) is also analyzed in the framework of category theory. It is shown that the category of rough sets is isomorphic with the category of so-called rough 4-valued sets. It happens that an object isomorphic with a rough set need not be a rough set itself.
Artificial intelligence, lattice of rough subsets, rough sets, Heyting algebra, Set theory, pseudo-Boolean algebras, Boolean algebra, category of rough sets, Logical aspects of lattices and related structures
Artificial intelligence, lattice of rough subsets, rough sets, Heyting algebra, Set theory, pseudo-Boolean algebras, Boolean algebra, category of rough sets, Logical aspects of lattices and related structures
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