Dependency Measures,Granulation Characteristics,Attribute Reducts Of Two Types Of Fuzzy Rough Sets Based On Double Quantization And Three-way Decision

Fuzzy rough sets are a generalization of classical rough sets,and they demonstrate uncertainty robustness and application adaptability by virtue of fuzzy similarity relations to be capable of handling symbolic,numerical and mixed data.This fact makes fuzzy rough sets provide a powerful processing method for complex data sets containing uncertain information.In practical applications,the knowledge in uncertain intelligent information system often comes from multiple channels,even from new application background,and this makes the applications and extensibilities of fuzzy rough sets be greatly limited.Therefore,this thesis studies models of multi-granulation fuzzy rough sets and divergence-based fuzzy rough sets from three aspects,including dependency measures,granulation characteristics and attribute reduction.With the help of double quantization and three-way decision,a comprehensive and detailed analysis of information from different sources can be realized,as well as the application value in the innovation scene.Specific research contents are listed as follows.For multi-granulation fuzzy rough sets,firstly,based on the fusion double quantization technique,the maximum membership degree and minimum membership degree are linearly combined in the multi-granulation fuzzy rough set model,and a generalized multi-granulation membership degree with weighted parameters is constructed.Based on three-way decision,the membership degree can stimulate the DT-MFRSs model and its corresponding three-way regions.At the same time,the attitude preference values of 1,0 and 0.5 in the membership degree produce optimistic,pessimistic and compromise DT-MFRSs models,respectively.Secondly,the membership degree and the non-monotonicity and uncertainty of the three-way regions are analyzed.These basic characteristics can induce the reduction criteria under the new regionpreserving strategy.At the same time,the three-way reduction criteria and their systematic relations are proposed through the positive,negative and positive-negative region-preserving strategy.Finally,the results of measures,models and reductions are validated by table examples and data experiments.For divergence-based fuzzy rough sets,firstly,based on the divergence matrix and the lower approximation matrix,the bidirectional double quantization and three-way decision are used to propose bidirectional three-level dependency measures.They are absolute dependency degree and relative dependency degree,respectively.Secondly,the corresponding attribute significance is induced by the bidirectional three-level dependence measures,and the granulation monotonicity of absolute and relative measures and the granulation non-monotonicity of absolute and relative attribute significance are studied,respectively.Thirdly,the double-quantization attribute reduction algorithms FS-AFS and FS-RFS are designed with the discussion of the absolute attribute significance and relative attribute significance.Finally,examples are given to prove the granulation characteristics of dependence degree and attribute significance,and the effectiveness of the double-quantization attribute reduction algorithms are verified by data experiments.