On The Model Of Graded Rough Intuitionistic Fuzzy Set Based On Dominance Relation And Its Application

Rough set theory is based on exact classification.However,in the real world,this condition is too harsh and limits its application range.Besides,rough set also have many other extended models,such as graded rough set,multi-granulation rough set,and two-universe rough set.Yao consider the quantitative information of the overlap of the set X and the equivalence class proposing graded rough set model.Graded rough set's upper and lower approximations are defined according to how much X overlaps with the equivalence class.Among them,the multi-granulation rough set can better solve the multi-granulation problem in reality.The intuitionistic fuzzy set promoted by Professor Atanassov,which gives the membership degree,non-membership degree and hesitancy degree,can better handle uncertain,incomplete information.In addition,since both intuitionistic fuzzy set and rough set can deal with uncertain and incomplete information,the two theoretical considerations are different from the angle and focus,so they have strong complementarity.Therefore,a scholar has combined two theories proposing the rough intuitionistic fuzzy set theory.However,the rough intuitionistic fuzzy set is also based on accurate classification,which also limits its application range.For this problem,from the perspective of the dominance relation,this paper combines the graded rough set and the intuitionistic fuzzy set constructing a graded rough intuitionistic fuzzy set model based on dominance relation.Based on the intuitionistic fuzzy order information system,the graded rough intuitionistic fuzzy set model based on the dominance relation is extended from the perspective of multi-granulation and two-universe.The related multi-granulation and two-universe models are established.The properties of these models are discussed.The validity of the model is verified by some examples.The main research work of this paper is as follows:(1)Aiming at the classification limitation of classical rough set,based on the rough intuitionistic fuzzy set model,a graded rough intuitionistic fuzzy set model is proposed.Firstly,the graded rough set based on dominance relation is defined.Combined with the dominance relation on intuitionistic fuzzy order information system with the dominance relation on graded rough set,the I-type dominance relation and II-type dominance relation are proposed.Based on I-type,II-type dominance relation,graded rough intuitionistic fuzzy set based on I-type,II-type dominance relation are proposed.From the perspective of multi-granulation theory,graded rough intuitionistic fuzzy set based on I-type,II-type dominance relation are extended to multi-granulation graded rough intuitionistic fuzzy set based on I-type,I-type dominance relation.Finally,the related properties of these models are discussed,and the validity of these models is proved by examples.(2)For the rough intuitionistic fuzzy set model,the largest and smallest membership degree and non-memberships degree are used to get the upper and lower spproximation,and the role of the elements between the largest and smallest membership degree and non-membership degree is ignored.Defining(?)(y)and (?)(y),we construct the new lower and upper approximations.And we have four proposed models.They are type-I,type-II graded rough intuitionistic fuzzy set models based on dominance relation and type-I,type-II two-universe graded rough intuitionistic fuzzy set models based on dominance relation.We discuss the relevant properties of these models.Finally,the boundary of the proposed models is reduced by the example verification,and the fuzzy entropy value is also reduced.(3)Based on the graded rough set based on dominance relation,the algorithm of the car's attribute is designed by analyzing the related attributes of the car,and the system framework is constructed based on the user's requirements.Finally,a car recommendation system based on the graded rough set based on dominance relation is established.By dealing with the user's demand for car related attributes,the system recommends a series of models with the best price/performance ratio and provides a better solution for users to purchase cars.Finally,an example is given to demonstrate the effectiveness of the system.