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.
Fund:Supported by National Natural Science Foundation of China (No.61573321), Natural Science Foundation of Zhejiang Province (No.LY14F030001,LZ12F03002),Scientific Research Start-up Fund of Zhejiang Ocean University (No.21065014715)
About author:: (TAN Anhui(Corresponding author), born in 1986, Ph.D., lecturer. His research interests include granular computing, concept lattice and uncertainty theory.)(LI Jinjin, born in 1960, Ph.D., professor. His research interests include artificial intelligence, granular computing and topology.)(WU Weizhi, born in 1964, Ph.D., professor. His research interests include artificial intelligence and information theory.)
TAN Anhui,LI Jinjin,WU Weizhi. Approximation and Reduction Relationships between Multi-granulation Rough Sets and Covering Rough Sets[J]. , 2016, 29(8): 691-697.
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2016, Vol. 29 
