Research On Extension Models Of Soft Set And Its Applications In Decision Making

The soft set is a mathematical theory to solve the problem of insufficient parameters of the fuzzy set,and also an effective mathematical tool for dealing with uncertainty.Based on the existing research results,the three extension models of fuzzy soft sets are further explored in the thesis,they respectively are fuzzy soft sets and intuitionistic fuzzy soft sets and bipolar fuzzy soft sets.Firstly,based on the fuzzy soft set and intuitionistic fuzzy soft set,the strong weak fuzzy soft set and strong weak intuitionistic fuzzy soft set respectively are proposed in the thesis,and their related properties are discussed.Secondly,the new similarity measure method in intuitionistic fuzzy soft set is studied,and the new similarity measure method is applied to the decision-making problem.Thirdly,the new bipolar fuzzy soft set is studied,its operation is defined and related properties are studied.In the end,the similarity measure method of the new bipolar fuzzy soft set is studied,and the method is applied to the decision-making problem.The details are as follows:(1)The operation of fuzzy soft set is analyzed and studied.Firstly,the fuzzy soft set of different parameters is analyzed from the angle of parameter information,and the concept of strong and weak fuzzy soft set are proposed.On the basis of the definition and the relationship between the two definitions,the operation properties of the two definitions are given,and the operation properties of the two definitions are given to satisfy the de-morgan law.These two explanations make the operation come in pairs,which makes the operation simpler and easier to understand,so that the operation is unified under the same theoretical framework.Finally,the research results of fuzzy soft sets are promoted to intuitionistic fuzzy soft sets.(2)Based on the intuitionistic fuzzy soft set,a new method of similarity measurement is presented.On the basis of the inclusion degree and similarity of the intuitionistic fuzzy set in the complete bounded lattice,the inclusion degree and the axiom of similarity of intuitionistic fuzzy soft sets are put forward.Based on the formula of the inclusion degree of intuitionistic fuzzy sets,the inclusion degree formula of intuitionistic fuzzy soft sets with different parameter sets is constructed.Based on the similarity definition of intuitionistic fuzzy soft set,the similarity formula of intuitionistic fuzzy soft set is constructed by using the inclusion degree formula of intuitionistic fuzzy soft set.Finally,a decision method is constructed based on new similarity measure method of intuitionistic fuzzy soft set,and applied to the judgment of the security situation in tunnel after the earthquake disaster,then the feasibility and validity of the method are explained.(3)The bipolar fuzzy soft set is studied.In the thesis,the two extremum soft sets are further promoted by using the information of the parameter set,and the double extremum soft set is integrated into the fuzzy set,and a new concept of fuzzy soft set is proposed.On the basis of this,the extensional definition of double extremum fuzzy soft set is given,including expansion intersection and union,strict intersection and union,and,or,the definition of the six kinds of operation and its related operation property is given,and the operation property are proved.Finally,a kind of reduction algorithm is used to make the decision of the optimal fund choice.(4)The inclusion degree and similarity of bipolar fuzzy soft sets are studied.Firstly,the inclusion degree of dual extremum fuzzy set is defined and the inclusion degree of different forms is presented.Secondly,the inclusion degree and similarity in the bipolar fuzzy soft set is given,and the inclusion degree formula of the fuzzy soft set is constructed by using the inclusion degree formula of the bipolar fuzzy sets with different forms;Then,according to the axiomatic definition of similarity,the formula of similarity of different forms is constructed by combining the inclusion degree formula of the fuzzy soft set.Finally,a decision method is constructed based on the similarity of the fuzzy soft set of bipolar value,and this method is applied to diagnosis of mental illness.