Topological properties of generalized approximation spaces. (English) Zbl 1242.68342

Yang, Lingyun; Xu, Luoshan

Inf. Sci. 181, No. 17, 3570-3580 (2011).

Summary: Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concepts of rough set theory are information systems and approximation operators of approximation spaces. Approximation operators draw close links between rough set theory and topology. This paper concerns generalized approximation spaces via topological methods and studies topological properties of rough sets. Classical separation axioms, compactness and connectedness for topological spaces are extended to generalized approximation spaces. Relationships among separation axioms for generalized approximation spaces and relationships between topological spaces and their induced generalized approximation spaces are investigated. An example is given to illustrate a new approach to recover missing values for incomplete information systems by regularity of generalized approximation spaces.

MSC:

68T37	Reasoning under uncertainty in the context of artificial intelligence
54D10	Lower separation axioms (\(T_0\)–\(T_3\), etc.)
54D15	Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
54D30	Compactness
54D05	Connected and locally connected spaces (general aspects)

Keywords:

approximation space; rough set; information system; preorder; separation axiom; compactness

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