The Approximation Of Membership Function Of Fuzzy Numbers

Fuzzy set theory is an accurate description of fuzzy information theory.A special fuzzy set,that is,the fuzzy number,once is generated and widely used in each engineering field.The study of fuzzy numbers is usually based on membership function,but for relatively complex fuzzy numbers,we cannot quickly and accurately understand their properties.As a result,many mathematical scholars use the approach of approximation method,that is,they use conventional fuzzy number functions to approximate the relatively complex fuzzy numbers,which open up a new research topic of fuzzy number approximation the door.The problem of fuzzy numbers of approximation has successfully attracted many scholars,and they have received important scientific research results.Scholars commence study the approximation of general fuzzy numbers from triangular fuzzy numbers,then scholars study the approximation of the general fuzzy numbers by trapezoidal fuzzy numbers and weighted triangular fuzzy numbers.This thesis is inspired by the literature of[38] and [42],we found a new research point.In the conditions for the 1-1 ordinate nodes and multiple nodes,the membership function of the broken line fuzzy number is used to approximate the general fuzzy number,and the approximate calculation of the broken line fuzzy number is studied its nature.Followed by knowing the simple fuzzy number,we have try to increase the number of nodes horizontal with the approximate operator of a simple fuzzy number,what happen to the approximate operator of a simple fuzzy number quality.This thesis is organized as follows:1.In Chapter 1,we,briefly,introduce development background of fuzzy numbers and research status of fuzzy numbers approximation problem.2.In Chapter 2,we,mainly,introduce basic concepts of fuzzy set theory,related concepts and properties of fuzzy numbers.In particular,definitions of several special fuzzy numbers are introduced for the following chapters.3.In Chapter 3,first of all,when ordinates of the nodes are known,we use the broken line of 1-1 nodes to find the method of approximating the general fuzzy number.Secondly,based on the literature [38],we use the r-s-nodes broken line fuzzy number to approximate the general fuzzy number and find its approximate approach to the general fuzzy number.4.In Chapter 4,first of all,basing on the membership functions of simple fuzzy numbers,the nodes of approximation operators are discussed in detail and the related results are obtained,under the condition of the abscissas set of nodes.Secondly,according to the conclusion of r-s-nodes broken line fuzzy number approximation,we define the approximation operator of r-s-nodes broken line fuzzy number.Finally,we prove some properties of the approximation operator.5.In Chapter 5,We sum up the paper and look forward to what we can do in the future.