Distance On Fuzzy Ellipsoid Number Space And Application

Professor L.A.Zadeh put forward the concept of fuzzy set in “Fuzzy sets” for the first time in 1965.As a result,it opened up a new discipline.In 1972,Zadeh and Chang introduced the concept of fuzzy number,which has opened up a new field of the research of fuzzy number theory.With the deepening of the research on the theory of fuzzy number,more and more research results have been showed.Nowadays,the theory of fuzzy number has become an important research direction of the theory of fuzzy set.Fuzzy celln-numbers is a special fuzzy numbers and it can be used to deal with some application problems with the feature of imprecise or uncertainty information.And it has the strong application background.However,fuzzy celln-numbers will miss some important information and do not tally with the actual while it is used in representing some information with imprecision or uncertainty.Wang put forward the concept of fuzzy ellipsoid number for the first time in 2013.And he gave the definition of n dimensional ellipsoid number.With fuzzy n-ellipsoid numbers be able to more objective and more rational than using fuzzy celln-numbers in representing uncertain multi-channel digital information than fuzzy celln-numbers,we need to study the fuzzy n-ellipsoid numbers for further exploration.In order to reveal the difference between two different fuzzy ellipsoid numbers,we give the definition of some new metrics on fuzzy ellipsoid numbers space,discussed their properties and relationship between each other.What's more,its application to the evaluation of urban life.We will show the main works of this paper as follows:1.In chapter 1,we introduce the research background of fuzzy set,research status of fuzzy n-ellipsoid number and the arrangement of the main content.2.In chapter 2,we mainly introduce the basic concept,algorithm of fuzzy set and fuzzy n-ellipsoid number and their properties.3.In chapter 3,we give the definition of some new metrics on fuzzy ellipsoid numbers space,discussed their quality and relationship between each other.4.In chapter 4,on the basis of studying the properties of metrics on fuzzy n-ellipsoid number space in chapter 3,we discuss some properties about the metrics sD on two kinds of special fuzzy ellipsoid number space?5.In chapter 5,on the basis of studying the properties of metrics on fuzzy n-ellipsoid number space in chapter 3,we not only introduce the concept of supremum(infimum)of bounded subsets on fuzzy ellipsoid number space,but obtain its concrete calculation formula.Then,by using the obtained results,we put forward a method to ranking multi-dimensional imprecise or uncertainty information,and give a practical example to show its rationality.6.In chapter 6,we primarily summarize this paper,and looking forward to the future of the research work at the same time.