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Neighborhood operator systems and approximations. (English) Zbl 1019.68109

Summary: This paper presents a framework for the study of generalizing the standard notion of equivalence relation in rough set approximation space with various categories of \(k\)-step neighborhood systems. Based on a binary relation on a finite universe, six families of binary relations are obtained, and the corresponding six classes of \(k\)-step neighborhood systems are derived. Extensions of Pawlak’s rough set approximation operators based on such neighborhood systems are proposed. Properties of neighborhood operator systems and rough set approximation operators are investigated, and their connections are examined.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
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