The Extension And Application Of Type-2 Fuzzy Set

With the increasing complexity of the problems encountered in daily life,the decision-making environment becomes more fuzzy.It is difficult to determine the values of membership functions in a real number of[0,1].The type-2 fuzzy theory has been discussed to deal with more complex problems.In this dissertation,the type-2 fuzzy sets are proposed to deal with the powerful processing power of language information.We take the type-2 fuzzy set and decision method as the breakthrough point,and combine the theory of soft set and cross entropy to extend and apply it.This article is divided into three parts,the main research results are listed as follows:The first extension of the type-2 fuzzy set:the basic concepts,properties and operators of the classical fuzzy sets and type-2 fuzzy sets are introduced.The type-2 fuzzy set is extended to the type-m fuzzy set of higher dimension,and a new definition of type-m fuzzy set is developed,and the simple operation properties of the type-m fuzzy set are discussed.The second extension of the type-2 fuzzy set:the special case of the type-2 fuzzy set,that is,the interval type-2 fuzzy set,and the multi-attribute group decision making problem in interval type-2 fuzzy environment is studied.A new definition of interval type-2 fuzzy cross entropy is put forward,which contains three aspects of fuzzy,hesitation and interval information.On this basis,a novel interval type-2 fuzzy entropy is proposed.According to the information of optimization theory and attribute weight,we establish two ranking-entropy optimization decision models,and a new method of multi-attribute group decision making for dealing with interval two type fuzzy sets is given.Finally,an example is given to verify the feasibility and effectiveness of our method.The third extension of the type-2 fuzzy set:the decision information with high uncertainty,we combine the type-2 fuzzy sets with the soft sets,a new definition of type-2 fuzzy soft sets is proposed,which is called soft type-2 fuzzy sets.On this basis,the definition of soft type-m fuzzy set is introduced,and the soft type-m fuzzy set and its properties are discussed.The interval type-2 fuzzy number is the extension of the type-2 fuzzy number,so the definition of the soft interval type-2 fuzzy set is given.Finally,a multi-attribute decision making method of soft interval two type fuzzy set is given.The feasibility and effectiveness of the method are verified by an example.