Approximation and Reduction Relationships between Multi-granulation Rough Sets and Covering Rough Sets
TAN Anhui1,2, LI Jinjin3, WU Weizhi1,2
1.School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022 2.Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province,Zhejiang Ocean University, Zhoushan 316022 3.School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000
Abstract：Multi-granulation rough sets and covering rough sets are two important mechanisms of data processing. From the viewpoint of approximation and reduction, therelationship between multi-granulation rough sets and covering rough sets in complete and incomplete information systems are discussed. Through constructing a space of granules of an information system, it is proved that the optimistic and pessimistic multi-granulation approximations are equivalent to the loose and tense covering approximations, respectively. It means that the optimistic and pessimistic multi-granulation rough sets can be represented by the loose and tense covering rough sets, respectively. Furthermore, two types of consistent sets in multi-granulation rough sets can be transformed into two types of consistent sets in covering rough sets, and there are close relationships of reduction between multi-granulation rough sets and covering rough sets.
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2016, Vol. 29 
