Research On Three-way Decisions Models Of Multi-granulation Rough Intuitionistic Fuzzy Sets

The three way decisions theory is a new mathematical tool for dealing with uncertainty.Because the three-way decisions theory is more in line with human choice habits and can better explain the semantics of decision-theoretic rough sets theory,it has become a new research hotspot in the near future.In addition,intuitionistic fuzzy sets,as a mathematical tool for processing fuzzy information,are also used to deal with uncertainty,so that decision makers can get more decision-making behavior in line with human thinking in the process of describing the fuzzy concepts of "neither one nor another" and "neutral concept betwixt".The multi-granulation rough sets theory is a mathematical framework for dealing with granular computing.How to make optimal granular selection and obtain more accurate information in information particles has become one of the important research directions.The combination of the intuitionistic fuzzy sets and the three-way decisions theory,considering the internal ambiguity of each granularity,the external redundancy granularity and internal redundant objects of the multi-granularities can be deleted,and a more reasonable optimal granularity decision-making scheme can be obtained.Therefore,how to use the theories of multi-granulation rough sets and intuitionistic fuzzy sets to study the model extension of three-way decisions and the optimal granularity selection scheme has certain significance.On the basis of multi-granulation rough sets and intuitionistic fuzzy sets,combined with the concept of three-way decisions,this paper studies the theoretical expansion and model construction of three-way decisions.Firstly,two new granularity importance measurement formula are defined,and a granularity reduction algorithm based on these methods is designed.A new three-way decisions model is constructed,which reduces the external redundancy information of granularity.Then,the reduced sets and intuitionistic fuzzy sets are combined to construct four new three-way decisions models based on multi-granulation rough intuitionistic fuzzy sets,which reduces the internal redundancy information in the reduced sets.The main contents of this paper are as follows:(1)In view of the problem that the existing granularity importance only considers the direct influence of single granularity on the decision-making,on the basis of the approximate quality of multi-granulation rough sets,the direct and indirect influence of the remaining granularities on the decision-making after removing a certain granularity is comprehensively considered.In this paper,a new measure of granularity importance degree is constructed,and a new algorithm of granularity reduction is given.By substituting reduction set into loss function,a new three-way decisions model based on granularity importance is obtained,which reduces the external redundancy information of granularity,and a corresponding comparison example is given.(2)Aiming at the problem of internal redundant objects in each granular of reduction set,four new multi-granulation rough intuitionistic fuzzy sets models are constructed by combining optimistic and pessimistic multi-granulation with intuitionistic fuzzy sets,and their related properties are discussed.On this basis,in order to further reduce the internal redundant objects in each reduction set,four new three-way decisions models based on multi-granulation rough intuitionistic fuzzy sets are constructed.For the purpose of obtaining the optimal granularity selection results,we define a comprehensive score function and a comprehensive accuracy function.Finally,the validity of the model is verified by a series of algorithms and examples.This paper expands the three-way decisions theory by studying the optimal granularity selection method of multi-granulation rough sets.First,a novel three-way decisions model based on granularity importance degree is constructed.And extending it to intuitionistic fuzzy environment,four new three-way decisions models based on multi-granulation rough intuitionistic fuzzy sets are designed to obtain the optimal granularity selection results.