Centroid Of High Dimensional Fuzzy Numbers And Its Application

With the continuous progress of the society and the continuous development of sci-ence and technology,the processing of mutil-channel uncertain digital information such as sorting,identification and classification is becoming more and more important in the field of engineering.In this paper,based on the definition of centroid of high dimensional fuzzy numbers,the expressions of two special fuzzy number(i.e.fuzzy n-cell number and fuzzy n-ellipsoid number)in definite integral form are obtained by relevant deriva-tion,and their relevant properties are studied.Then,an aggregation operator(i.e.fuzzy order)for ordering fuzzy number is proposed,and a dynamic sorting method based on the aggregation operator is given.Finally,an example of "enterprise evaluation ranking" is given to illustrate the proposed dynamic ranking method based on fuzzy order.In Chapter 1,the research and development of fuzzy number and aggregation opera-tors in fuzzy number space are summarized.In Chapter 2,the relevant basic concepts and properties of fuzzy sets and fuzzy Numbers are introduced,as well as the concepts and properties of fuzzy n-cell numbers and fuzzy n-ellipsoid numbers.In Chapter 3,The membership function of high-dimensional fuzzy number is regard-ed as the density function on the closure of its support set,the concept of the centroid of n-dimensional fuzzy number is proposed by us and the expression of centroid of high dimensional fuzzy number is given,and its properties are discussed.In Chapter 4,We restrict the general n-dimensional fuzzy number to the fuzzy n-cell number space,and by using the special properties of fuzzy n-cell number,we get the centroid expression of definite integral form which is easy to calculate and discuss the properties of centroid of fuzzy n-cell number.Then,considering the extensive application of triangular fuzzy number in the field of engineering,by using the special properties of triangular fuzzy number,we obtain the centroid expression of a special fuzzy n-cell number(i.e.n-dimensional pyramidal fuzzy number).In Chapter 5,In order to overcome the shortcomings of fuzzy n-cell number in rep-resenting multi-channel uncertain digital information,we limit the general n-dimensional fuzzy number to the fuzzy n-ellipsoid number space,and by using the special proper-ties of fuzzy n-ellipsoid number,we obtain the centroid expression of fuzzy n-ellipsoid number.Then,an aggregation operator(i.e.fuzzy order)for fuzzy number ordering is introduced and its properties are discussed.Finally,a dynamic ranking method based on the fuzzy order is established,and an example of "enterprise evaluation ranking" is given to illustrate the implementation of the proposed dynamic ranking method in detail.In Charter 6,the main word of this paper is briefly summarized,and the relevant contents to be studied in the future are prospected.