Quasi-discrete Fuzzy Number And Its Application

Since the Pareto efficiency was proposed,the idea of multi-attribute decision-making has been integrated into all fields of people’s life.The more complex the things exist,the more fuzzy they are.It is difficult to screen the inaccurate and fuzzy information when making multi-attribute decision.And how to effectively solve the fuzzy multi-attribute problem has become extremely important for the current social work.In this thesis,the concept of quasi-discrete fuzzy number and its vector is proposed.The text discusses the representation theorem and properties of quasi-discrete fuzzy numbers,defines the centroid of quasi-discrete fuzzy numbers and their vectors,and establishes the weak order on the vector space of n-dimensional discrete quasi-fuzzy numbers.Based on the established weak order relation,a method of constructing n-dimensional discrete quasi-fuzzy number vector is proposed to ranking multi-channel uncertain integer quantity digital information.On the other hand,a fuzzy order relation is established on the n-dimensional discrete quasi-fuzzy number vector space,based on the fuzzy ordering relation,we establish a dynamic ranking method for multi-channel uncertain digital information(the method makes the ranking result change with the change of level value).Our main research process for this thesis is divided into the following chapter:1.In the first chapter,looking back on the development of fuzzy number and discrete fuzzy number,this thesis discusses the sorting of fuzzy number in general.we review the development of fuzzy numbers and discrete fuzzy numbers,and discuss the ranking problems of fuzzy numbers.2.In the second chapter,the notions and theorems of fuzzy sets and fuzzy numbers are briefly introduced,and their properties are discussed.The text reviews the concept and theorem of discrete fuzzy number,and discusses some properties related to it.It is also a preparation for our future research.3.In the third chapter,the concept of quasi-discrete fuzzy number and its vector is given.This thesis discusses the representation theorem and properties of quasi-discrete fuzzy numbers,defines the centroid of quasi-discrete fuzzy numbers and their vectors,and establishes the weak order on the vector space of n-dimensional discrete quasifuzzy numbers.Based on the established weak order relation,a method of constructing n-dimensional discrete quasi-fuzzy number vector is proposed to ranking multi-channel uncertain integer quantity digital information and applied in an example.4.In the forth chapter,we define a fuzzy order on the space of n-dimensional discrete quasi-fuzzy number vector by using the centroid of quasi-discrete fuzzy number vector established in Chapter 3,which is applied to compare the advantages and disadvantages of two fuzzy number vectors.The reason why fuzzy order is introduced is that a method of constructing n-dimensional discrete quasi-fuzzy fuzzy number vector is proposed in Chapter 3 to ranking multichannel uncertain integer quantity digital information.On the basis of this method,it not only compares the size relationship between two vectors,but also gives the advantages and disadvantages of the two fuzzy vectors.5.In the fifth chapter,the contents of the previous research are summarised,and on the basis of the existing research,the future research content is proposed.