Rough Sets and Brouwer-Zadeh Lattices

Many researchers study rough sets from the point of view of description of the rough set pairs (a rough set pair is also called a rough set), i.e. . In this paper, it is showed that the collection of all the rough sets in an approximation space can be made into a distributive Brouwer-Zadeh lattice. The induced Brouwer-Zadeh lattice from an approximation space is called the rough Brouwer-Zadeh lattice. The rough top equation and rough bottom equation problem is studied in the framework of rough Brouwer-Zadeh lattices

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