Two Kinds of Rough Algebras 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. . Comer [4] showed that all the rough sets in an approximation space constructed a regular double Stone algebra. The constructed algebra is called the rough double Stone algebra in this paper. Pagliani [19] interpreted Rough Set System (all the rough sets in an approximation space in disjoint representation) as a Nelson algebra. The constructed Nelson algebra from an approximation space is called the rough Nelson algebra in this paper. It is showed that a rough double Stone algebra is a Brouwer-Zadeh lattice, and a rough Nelson algebra is a Brouwer-Zadeh lattice also.

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