The Supremum And Infimum Of Discrete Fuzzy Number Sets And High Dimensional Discrete Fuzzy Numbers

Since the generation of fuzzy numbers,it has been applied to every aspect of the engineering filed,it also shows the function of fuzzy number.In the actual production and life,we should not only solve the problem of boundary uncertainty continuous quantity,but also solve the problem of discrete quantity of boundary uncertainty.Like a flock of birds,a basket of apples,a forest.Therefore,to study and solve the discrete boundary uncertainty fuzzy number problem is particularly important,and within the scope of this research,we have arrived at some good conclusions.In the field of mathematics,the continuous fuzzy numbers and the discrete fuzzy numbers are special fuzzy sets on the real number sets,and there have been a lot of achievements on the theory and application of fuzzy numbers.Discrete-type fuzzy number problem is an important research topic,which has a strong practical background,and has obtained many important conclusions about the discrete fuzzy number.The main contents of this paper are divided into two parts.The first part is mainly about the existence and the exactness of the upper and lower bounds of one-dimensional continuous fuzzy numbers and n-ellipsoid fuzzy spaces and of bounded sets in fuzzy integer spaces We discuss the existence and representation of the upper and lower bounds of bounded sets on the quasi-finite set in the discrete fuzzy number space.The second part is based on the obtained low-dimensional discrete fuzzy number theory gives the definition of highdimensional discrete fuzzy number and its related properties.The main contents of this papper are as follows:1.In chapter 1,we mainly introduce the background information related to the main discussion of this thesis.2.In chapter 2,we mainly introduce the basic theoretical knowledge of fuzzy numbers and fuzzy sets.3.In chapter 3,based on the inclusion relation of fuzzy sets,the concept of partial order in discrete fuzzy number space is proposed,and the representation theorem of discrete fuzzy numbers is obtained.The existence of the Supremum and Infimum of bounded sets of discrete fuzzy numbers in space is proved.The expressions of the upper and lower bounds are obtained.4.In chapter 4,based on the theory of low-dimensional discrete fuzzy numbers,by introducing a theorem,we introduce the definition of high-dimensional discrete fuzzy numbers.Then,we give a special high-dimensional discrete fuzzy number which is more convenient to use.We discuss the correlation properties of high-dimensional discrete fuzzy numbers and the mean of high-dimensional discrete fuzzy numbers,and then establish a weak order in a high-dimensional discrete-valued fuzzy number space on the mean,and give an example to illustrate the weak order The rationality.5.In chapter 5,we summarize the full text,and look forward to the content steps to be discussed in the future.