Ranking Problems On Fuzzy Number Space

Multi-attribute decision-making(MADM)is an important component of human life.It involves many problems in reality.From the initial research to the present,The classic multiple attribute decision making has been almost perfect.With the development of society and economy,fuzziness and complexity of things increased,which makes the multiattribute decision making problem is uncertain and fuzzy,so that's called fuzzy multiple attribute decision making.It is becoming more and more important that how to solve the fuzzy multi-attribute problem.And,when analysis of fuzzy multiple attribute decision making,we often describing preference of decision makers and attribute value of every program with fuzzy numbers.Therefore,comparisons between programmes usually come down to the ranking of fuzzy numbers.Since the last century,many scholars have conducted in-depth research on the ranking of fuzzy numbers,and have achieved a wealth of research results.In this thesis,a new ranking method of fuzzy numbers is proposed on the basis of previous studies.This thesis make fuzzy numbers and the results of fuzzy number comparison into the volume of the real axis based on the fuzzy membership function.In order to achieve a comparison between fuzzy numbers or a pair of fuzzy numbers.It is the point of penetration.From the perspective,We study the problem of ranking of some one-dimensional fuzzy numbers and n-dimensional fuzzy numbers.The main work of this thesis lie in the following:1.In the chapter 1,the background of fuzzy numbers,and the research status of ranking of fuzzy numbers are introduced.2.In the chapter 2,we introduced some concepts about fuzzy set and fuzzy numbers,several special fuzzy numbers are introduced especially for the following.3.In the chapter 3,based on membership function of fuzzy number,we defined a real amount as fuzzy number ranking index that can describe the merits of fuzzy numbers reasonably and objectively.This method is reasonable and convenient to calculate.And in view of some deficiencies in the method,we introduce the dispersion to improve the ranking index function we defined.Although the calculation is more complex than the previous methods,it is simple and convenient to operate also.Finally,based on the real quantity that can describe the merits of fuzzy numbers,the ordering index function of n-dimensional fuzzy number vector is given.4.In the chapter 4,we defined a fuzzy order in fuzzy number space of n-dimensional ellipsoid based on membership function of fuzzy number,it can compare pairs of fuzzy number.Ranking fuzzy numbers with fuzzy order which we defined,it can not only compare the fuzzy number,but also get the size of the degree of compare between fuzzy numbers.5.In the chapter 5,we summarize the article and prospect the problems to be studied in the article.