| In the research field of fuzzy numbers,the metric of fuzzy number play a very important role.Metrics of fuzzy numbers have been applied in data analysis in various areas such as fuzzy decision,fuzzy structural analysis,fuzzy clustering and so on.Thus,many scholars paid great attention and did some research on the metric of fuzzy number.But difference between membership function values were not considered,this may not be quite rational since at least syntactically higher membership values might be more important than the lower values,and the metric might better reflect such phenomena.In order to reflect the difference of membership degree on metrics of fuzzy numbers,we introduce a weighted metric L_ω and metric d_ω for fuzzy numbers in this paper.The full these is divided into four chapters.Chapter one is the introduction,this chapter reviews the history of the metric of fuzzy numbers and the development are figured out briefly.Chapter two is the basic notation and preliminaries.Symbols and definitions used in the thesis are given in thesis chapter.Chapter three is the main part of the thesis.In this chapter we study the weighted LP metric on fuzzy number space.We give condition on the weighted function w(α)under which the expression Lw is a metric on E~1,It is proved that L_ω is a metric on E~1 if and only for each subinterval I1 of I,∫I1ω(α)dα>0.We take one-dimensional space as an example to discuss completeness and separability of the weighted metric space(E~1,Lw).Secondly,we study the d_ω metric on fuzzy number space.We give condition on the weighted function ωn(α)under which the expression d_ω is a metric on E~1.Then we take one-dimensional space as an example to discuss completeness and separability of the weighted metric space(E~1,dw),and the character of the weighted metric space(E~1,dw)is discussed.Finally,relationship between the different weighted is given.In chapter four we summarize the thesis and give some suggestions for future study. |
