Analysis And Experimental Research On The Key Factors Of Determining Membership Function Of Fuzzy Sets

As an important mathematical tool to describe and process fuzzy information,fuzzy set has been widely concerned by many scholars from the fields of mathematics,engineering,economics and sociology since its birth.After more than 50 years of research and development,fuzzy sets have made great progress in both theory and application.At present,it has been widely used in such research fields as clustering analysis,image recognition,automatic control,artificial intelligence and so on.However,the theoretical basis of fuzzy sets is still very weak.Membership function is the core of fuzzy set theory,and the determination method of membership function is very important to the theory and application of fuzzy set.How to determine membership function of fuzzy set? How to determine the rationality of membership function? There is still no clear answer.In view of the above problems,Pan Xiaodong studied the essence of fuzzy phenomenon deeply,and established the axiomatic system of membership degree based on the new understanding of the essence of fuzzy phenomenon.On this basis,this paper through the design of statistical experiments,in-depth analysis of a number of key factors affecting the determination of fuzzy set membership function,in order to establish an objective experimental basis for the determination of fuzzy set membership function.Mainly completed the following three aspects of research work.Firstly,based on the essence of fuzzy phenomenon and the axiomatic definition of fuzzy set,considering whether vague partition has an impact on the determination of membership function of fuzzy set,the experiment is designed.After analyzing the data,it is found that vague partition affects the determination of membership function of fuzzy set.Secondly,considering the influence of space on the membership function of fuzzy sets,it is found that the membership function of the same fuzzy concept in different space is different,therefore,the membership function of fuzzy sets affected by space.Thirdly,based on the research on the method of determining membership function of fuzzy set,considering the difference of different methods to determine membership degree for the same fuzzy concept,based on this consideration,the design statistical experiment is carried out.Experiments show that for the same fuzzy concept,the membership degree of fuzzy statistical method and scoring method is similar.However,there are still some elements,and the membership degrees obtained by the two methods are quite different Finally,the stability of the two methods is analyzed.