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Topological properties of generalized approximation spaces. (English) Zbl 1242.68342
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 54D10 Lower separation axioms (${T}_{0}$–${T}_{3}$, etc.) 54D15 Higher separation axioms 54D30 Compactness of topological spaces 54D05 Connected and locally connected topological spaces (general aspects)