he College of Administration and Economics at the University of Baghdad discussed, a PhD dissertation in field of Statistics by the student (Rawya Emad Kareem) and tagged with (Estimation of the Fuzzy Liner Regression Model in the Presence of Multicollinearity Problem with the Application) , Under supervision of (Prof. Dr. Mohammed Jasim Mohammed )
When Estimating the Fuzzy Linear Regression Model, the model must have specific characteristics that depend on several assumptions, and in the absence of one of these assumptions, the model will suffer from some problems that make the estimation process wrong or sometimes not possible. Among these problems is the problem of multicollinearity. In the data and the lack of independence between the explanatory variables, where the data is interrelated, the existence of the problem of multicollinearity was revealed through the variance inflation factor (VIF) and the correlation matrix between the data, which proved the existence of a relationship between the variables; that is, there is a problem of multicollinearity. To address this problem, the fuzzy ridge regression (FRR) method, the fuzzy LASSO regression method (FLR), and the fuzzy bridge regression (FBR) method were used to estimate the parameters of the fuzzy linear regression model and choose the best method using several criteria for each road.
Where the process of estimating the parameters of the fuzzy regression model is using the trigonometric membership function, and the methods are compared with the Fuzzy Least Squares Estimator (FLS) method, which is a basic criterion for measuring air pollution. Whether it is good, acceptable, or bad for sensitive people
or dangerous through six factors (CO2, O3, SO2, pm10.pm2.5, NO2), which are measured in the air using stations spread in all governorates, during which their percentages are measured in the air, and data were taken for the month of November of the year 2020, by taking three readings per day, for all governorates, with an average of (8) hours. The data were tested to confirm the problem of multicollinearity and to formulate a model that represents the phenomenon of pollution in the governorates of Iraq using the statistical program R, and the results proved that the best method is the fuzzy letter regression method.
And using simulation, data were generated and samples were taken with different sizes (20, 40, 80, 160). Where the best model achieves the least value of the mean square error (MSE), where the results showed that the best model is the Fuzzy Ridge Regression method among the studied methods. It indicates the efficiency of the proposed method.