Research On The Extension Of Application Of Hesitant Fuzzy Set Models

With the advancement of society,life is full of uncertain knowledge and problems,and various research methods and advanced technologies emerge one after another.Uncertain mathematical theory has emerged as a means of solving problems.In this field of research uncertainty,fuzzy sets and rough set theory are the most classic models,and many scholars have conducted research on this basis.Hesitant fuzzy set is one of the general forms of fuzzy sets.The characterization of the tightness of elements and sets is accomplished by several values between 0 and 1,which can better reflect the hesitation of people or the uncertainty of events.However,in some cases,the existing hesitant fuzzy set model are not enough to deal with the ambiguity of the event itself.The numerical value is used to reflect the degree of accuracy less than the fuzzy set.Therefore,it is necessary to change the existing hesitant fuzzy set model.The method of characterization is optimized to better reflect the real situation of the event itself.Based on such specific problems,this paper study the existing hesitant fuzzy set model,in order to record,express and solve the complex and uncertain problems encountered in life,and also enrich the application of hesitant fuzzy set theory.The specific research contents are as follows:1.Firstly,the degree of subordination of elements and sets in the domain is replaced by multiple fuzzy sets,and a new model is defined as a type II hesitant fuzzy set,which aims to increase the ambiguity of the model.At the same time,the operation of this model is defined,and the order of the multiple fuzzy sets and the length of the hesitant fuzzy elements are specified.Then discuss the properties of this model,and then define several special type II hesitant fuzzy sets that will be used in subsequent research.2.Based on the type II hesitant fuzzy set model defined in the previous chapter,a type II hesitant fuzzy relation is proposed.By using this relationship to construct the correlation operator,a type II hesitant fuzzy rough set model is established.Then the model is analyzed,the rules of operator satisfaction are inferred,and the characteristics of the approximate operator of the model under different binary relations are analyzed.Then the upper approximation and the lower approximation of the hesitant fuzzy set of the type II under special relations are explored,and some equivalence propositions related to the special relationship are analyzed.3.The model is extended based on the type II hesitant fuzzy rough set defined above,and the domain is upgraded to the double domain.A type II hesitant fuzzy rough set based on the double domain is established.The nature of this model is then briefly studied.Then we briefly study the compounding of the double domain type II hesitant fuzzy relations and study its properties.Finally,it is proved by the case that the double domain type II hesitant fuzzy set model has certain application value.