A Survey on Axiomatic Characterizations of Rough Approximation Operators
WU Weizhi
School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022 Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan 316022
Abstract：Lower and upper approximation operators are the foundation in the study of theoretic aspect of rough set theory as well as its practical applications. One of the main directions of the theoretic study of rough sets is the axiomatic characterization of rough approximation operators. Based on various binary relations, constructive definitions of classical rough approximation operators, rough fuzzy approximation operators, and fuzzy rough approximation operators are firstly introduced. Axiomatic characterizations of these approximation operators are then summarized and analyzed. Finally, perspectives and comparison of rough set approximation operators with other mathematical structures are discussed.
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2017, Vol. 30 
