Research On Three-way Decisions Models And Its Application Of Double-quantitative Multi-granulation Rough Sets

Rough sets theory is a tool to deal with imprecise and uncertain problems.As it describes the concept of target from the perspective of single granulation,it has some limitations.However,multi-granulation rough sets theory can deal with more complex information systems by analyzing problems from multiple granulation through multiple binary relations.In addition,since the rough set based on the double quantization method was proposed,it has been widely concerned in uncertainty decision-making because of its comprehensive consideration of relative and absolute quantization information,which can improve the accuracy of approximate classification.The three-way decisions theory based on decision theory rough sets theory provides a reasonable semantic interpretation of rough regions of rough sets,and considers decision risk at the same time,making it a research hotspot of uncertainty decision-making.Due to the complexity and diversity of data,the limitation of data acquisition technology and the error of data measurement,the information obtained contains incomplete and inaccurate data.However,the uncertain knowledge hidden in these information systems is of great significance to decision-making.Therefore,it has certain significance and value to combine double quantitative multi-granulation rough sets with three-way decisions theory.Aiming at the problem of decision analysis in incomplete information system,the set-pair dominance relation is introduced in this paper.Based on multi-granularity rough sets and three-way decisions theory,the corresponding models are constructed to make decisions.Firstly,the multi-granularity space is extended,and the new upper approximate and lower approximate formulas of rough sets are defined.Then,the corresponding three-way decisions models are constructed based on the improved loss function.Moreover,for the variable precision rough sets and the graded rough sets,the two rough sets are further combined to get the double quantification rough sets models.Finally,the new three-way decision models based on the double quantification rough sets are constructed.The main contents of this paper are as follows:(1)In the multi-granularity decision rough sets,the set-pair dominance relation is introduced,and the set-pair dominance degree is improved to make the result more reasonable.Then,the multi-granulation approximation space is expanded,and five kinds of multi-granulation decision rough sets models under the set-pair dominance relation are proposed.In addition,the related properties and the relation among these models are discussed.Furthermore,combined with the theory of three-way decisions,the loss function is represented by interval value in incomplete information system,and different thresholds are obtained.Then five three-way decisions models are established,the corresponding three-way decisions algorithm is designed,and the decision rules are derived.Finally,the rationality and validity of the proposed models are verified by the case of employee evaluation.(2)Combined with the advantages of set-pair dominance relation and generalized multi-granularity,generalized multi-granularity set-pair dominance variable precision rough sets and generalized multigranularity set-pair dominance graded rough sets are proposed.Secondly,considering that the generalized multi-granularity set-pair dominance variable precision rough sets and generalized multi-granularity set-pair dominance graded rough sets describe the information from the relative and absolute perspectives respectively.The two rough sets are combined by logical disjunction and logical conjunction operators,and five double-quantification models are obtained,and the corresponding algorithm is constructed,which is verified by examples.Finally,experiments are carried out on the UCI data sets and compared with other complete models.The results show that the model is effective in dealing with practical problems.