Incomplete Multi-granulation Reduction Based on Discernibility Matrix
LIU Kai1,2, TAN Anhui1,2, GU Shenming1,2
1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan 316022 2. Key Laboratory of Oceanographic Big Data Mining and Appli-cation of Zhejiang Province, Zhejiang Ocean University, Zhou-shan 316022
Abstract：For the incomplete data with missing attribute values, the multi-granularity reduction structures of incomplete information systems and incomplete decision systems are constructed from the perspective of discernibility matrix. Firstly, the reduction attributes of incomplete information systems based on pessimistic and optimistic multi-granularity approximations are discussed, and three types of multi-granularity discernibility matrices of incomplete information systems and incomplete decision systems are constructed. Then, it is theoretically proved that all the multi-granularity reductions of incomplete information systems and incomplete decision systems can be computed accurately by the disjunctive and conjunctive logical operations of the constructed discernibility matrices. Finally, examples are given to demonstrate the effectiveness and practicability of the proposed method.
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2020, Vol. 33 
