Relevant Theories And Applications Of Fuzzy Transform Approximating Fuzzy Numbers

With the publication of "Fuzzy Sets",fuzzy concepts appeared in the field of vision of mathematicians.Fuzzy mathematics is also widely used in computer intelligence,system engineering,economic management,infrastructure engineering and other fields.With the broadening of research fields,those subjects that have nothing or almost nothing to do with mathematics in the past can also be expressed quantitatively by mathematical methods,which greatly expands the scope of application of mathematics itself.When we study fuzzy numbers,it is inevitable to study their membership functions.However,the membership function of fuzzy numbers is sometimes too complex and difficult to handle.Therefore,the related research on using fuzzy transformation to approximate fuzzy number is particularly important.This paper is mainly divided into four chapters,and the research content of each chapter is as follows:The main results of this paper are as follows:The first chapter is a general overview,which systematically clarifies the background of the topic selection,fuzzy approximation and fuzzy transformation research status.Based on the comprehensive analysis of previous studies,the research contents of each chapter of this thesis are drawn up.This paper generalizes the nature of fuzzy transformation based on the definition of generalized fuzzy partitions.Studying fuzzy partitions is the basis for studying fuzzy transformations.We can make various fuzzy partitions of a universe.In this paper,we will explore the properties of F-transform based on the definition of generalized Ruspini fuzzy condition.According to the relevant content of the F-transform(r=1 in this case)based on the definition of Ruspini conditional fuzzy partition,the basic functions of fuzzy r(r?1 and a fixed integer)partition,the general extension and properties of direct F-transform and inverse F-transform are studied.This paper discusses the approximation of fuzzy number value,ambiguity and expected interval.This chapter first introduces some relevant definitions and properties of fuzzy numbers and define the value,ambiguity and expected interval of the fuzzy number.we use the 1-norm to define the distance between any two fuzzy numbers.In addition,using the given continuous reduction function s and its definition of variable upper limited integral function S and continuous modulus ?(u,?)to help the approximation operation.Finally,some examples are given to illustrate that the accuracy of the result obtained by keeping the parameter approximation is higher.And then the relevant results are given.This paper has 4 charts and 81 references.