Robust MM Estimation Of Fuzzy Regression Model And Applied Research

In the research of regression analysis,the least square method is the most commonly used research method.Obviously and directly,its advantage is that it can find the best function matching of data by minimizing the sum of squares of errors in the case of satisfying the Gaussian-Markov assumption,which reduce computational complexity and calculate easier.However,the least square method is very sensitive to outliers in data.Even a single outlier will affect the estimation effect of the least square method.Based on those theories,many scholars have studied the influence of robust regression method in dealing with abnormal data.A commonly used method is Robust MM estimation method.which has the advantages of high collapse pollution rate and good estimation efficiency.In this paper,the robust MM estimation method is extended to the fuzzy regression model,and the fuzzy robust MM estimation is proposed.We compare the proposed method with four existing fuzzy robust regression methods,and the numerical simulation results our proposed method is the best among four of them.Finally,we apply fuzzy robust MM estimation to three practical examples,and get similar results to numerical simulation.Firstly,this paper looks back some foundational concepts of fuzzy regression and existing robust fuzzy regression methods.Firstly,it introduces the content of fuzzy numbers,involving membership functions,fuzzy sets and fuzzy operations,also describes the definition of fuzzy regression model in detail with the basic concepts of fuzzy numbers.The second part reviews four fuzzy regression models,including fuzzy least squares,weighted least squares fuzzy regression,robust fuzzy M estimation and robust fuzzy LTS estimation.Combining some basic concepts of fuzzy sets and robust fuzzy regression model,the robust MM estimation is extended to the fuzzy field.Even a new model is proposed,called robust fuzzy MM estimation.The definition and algorithm of robust fuzzy MM estimation are constructed,and some basic concepts are introduced.In order to prove that the model proposed in this paper has good properties,this paper verifies the model proposed via numerical simulation and practical application research.The numerical simulation is mainly analyzed from two angles: one-dimensional fuzzy regression analysis and multi-dimensional fuzzy regression analysis.Through Monte Carlo simulation,the robust fuzzy MM estimation proposed in this paper is compared with four existing robust fuzzy regression models,and abnormal data are added in x direction,y direction and x direction and y direction respectively for Monte Carlo simulation.The results show that the robust fuzzy MM estimation proposed in this paper is the best.In the practical application research part,the practical application research based on Monte Carlo simulation further proves the robust fuzzy MM estimation proposed in this paper.This chapter proves the effectiveness of the model proposed in this paper through three practical examples,and uses three fuzzy measures to measure the regression effect between the robust fuzzy regression model proposed and the existing robust fuzzy regression model.In practical examples.For the purpose of ensuring the reliability of regression analysis,firstly,the COOK distance is used to detect the outliers of three groups of data,and the detection results show that there are outliers in all three groups of data.Secondly,the robust fuzzy MM estimation method proposed in this paper and the existing robust fuzzy regression model are used to carry out regression analysis on three groups of actual data,and three measures are used to measure the analysis results for comparative analysis.Finally,Friedman test and Nemenyi test are compared and analyzed to further test the reliability of the results of Monte Carlo simulation and practical application research.The results show that the results of practical application research are similar to those of Monte Carlo simulation.In order to prove that the model proposed in this paper has good properties,this paper verifies the model proposed in this paper through numerical simulation and practical application research.The numerical simulation is mainly analyzed from two angles:one-dimensional fuzzy regression analysis and multi-dimensional fuzzy regression analysis.Through Monte Carlo simulation,the robust fuzzy MM estimation proposed in this paper is compared with four existing robust fuzzy regression models,and abnormal data are added in x direction,y direction and x direction and y direction respectively for Monte Carlo simulation.The results show that the robust fuzzy MM estimation proposed in this paper is the best.In the practical application research part,the practical application research based on Monte Carlo simulation further proves the robust fuzzy MM estimation proposed in this paper.This chapter proves the effectiveness of the model proposed in this paper through three practical examples,and uses three fuzzy measures to measure the regression effect between the robust fuzzy regression model proposed in this paper and the existing robust fuzzy regression model.In practical examples,in order to ensure the reliability of regression analysis,firstly,the COOK distance is used to detect the outliers of three groups of data,and the detection results show that there are outliers in all three groups of data.Secondly,the robust fuzzy MM estimation method proposed in this paper and the existing robust fuzzy regression model are used to carry out regression analysis on three groups of actual data,and three measures are used to measure the analysis results for comparative analysis.Finally,Friedman test and Nemenyi test are compared and analyzed to further test the reliability of the results of Monte Carlo simulation and practical application research.The facts deduce that the results of practical application research are similar to those of Monte Carlo simulation.