The Properties Of Special Fuzzy Number And The Approximation Of Fuzzy Number

Fuzzy theory is a tool to describe the fuzzy information,not a representation of”fuzzy mathematics”.Due to more complex fuzzy number,we can not understand its nature.To solve this problem,the researchers consider the approximation of fuzzy number with complex fuzzy number,and open a new chapter of the approximation of fuzzy number.As a new branch of fuzzy number,the approximation of the fuzzy number was born with a strong vitality and has attracted considerable attention.In the recent decade,people have studied the general fuzzy numbers,such as triangular fuzzy numbers,trapezoidal fuzzy numbers,etc.Using them,the approximation principle is based on the membership degree as the starting point,and the left and right point sets are obtained according to the minimum distance.In this dissertation,we mainly study the properties of simple fuzzy numbers structured by?Approximations of fuzzy numbers by step type fuzzy number?,and take the left and right point set of fuzzy numbers as the starting point to investigate the approximation of simple fuzzy numbers and their properties.The main contents are as follows:1.In Chapter 1,the generation and development of fuzzy numbers,the approximation of fuzzy numbers and the development are reviewed.2.In Chapter 2,we mainly introduce the binary relations on the fuzzy number space,and the types of common fuzzy numbers(triangular fuzzy numbers,trapezoidal fuzzy numbers)approximating to the general fuzzy numbers.It provides the basis for the theoretical knowledge of bedding.3.Chapter 3 introduces the operation properties,mean value and dispersion of simple fuzzy numbers,and also discusses the distance and difference between the simple fuzzy number and the general fuzzy number,and obtains the corresponding expressions based on its own characteristics.These expressions are not only easy to implement,but also easy to apply.4.In Chapter 4,we study the approximation between the simple fuzzy numbers and the general fuzzy numbers with known the left and right points sets.First,the positive definiteness of the Hessian matrix is used to judge the existence of the simple fuzzy number,which is approximate to the general fuzzy number.This approximation method is more meaningful than the previous approximation methods,one reason is that more information of the original general fuzzy number is retained;the second is that the calculation method is simple to operate and reduces the complexity of the calculation process;the third is that it provides another way of thinking the approximation of fuzzy number,that is,the left and right point set of fuzzy number can be set as the starting point,finally we define its approximation operator and study its properties.5.In Chapter 5,we summarize this thesis and give suggestions for some future work.