Research And Application Of Fuzzy Linear Regression Model With Normal Fuzzy Number

In 1982, Tanaka et al put forward the fuzzy linear regression model for the first time. This model takes the error between the observed value and the fitted value as the uncertainty of the system which is expressed as the fuzziness of the coefficients. Namely, the fuzzy linear regression model has fuzzy numbers of some membership function as its regression coefficients. Since the fuzzy linear regression model was put forward, it has become one of the research focuses of many scholars and it has been widely used in the field of engineering technology, economy, finance, management, biological science and so on. But among the existing researches, most scholars use symmetric triangular fuzzy number as coefficient of the fuzzy linear regression model and other types of fuzzy numbers are rarely discussed. Given in practice, many fuzzy phenomena can be described in normal fuzzy numbers. So it is necessary to study the fuzzy linear regression model with normal fuzzy number as its coefficient.This article main research content is as follows:First: Studying the multiple linear regression model based on normal fuzzy numbers systematically. In the least squares criterion, the solution of the model is decomposed into an unconstrained condition of least squares problem and a quadratic programming problem with linear constraint condition, and the existence and uniqueness of the solution is proved. Two evaluation indexes of the model are also given, they are fuzzy correction multiple correlation coefficient and average lattice degree of nearness, which are the merits of the evaluation model of regression and prediction effect.Second: After the outlier points processing by the means of classical linear regression model, apply the model studied in this article in the prediction of tin mineral resources reserves of some mine area and obtain the model as follow: Y^*=（73.1786,0）_N+（0.9065,0.2254）_NZ₁+（-0.9882,0）_NInZ₂+（0.6501,0.1290）_NInZ₃+（103881,0.3787）_NInZ₄+（0.521,0.063）_NZ₅Then the fuzzy adjusted-multiple correlation coefficient and the average lattice degree of nearness of the validation data are calculated respectively asR²=0.9004,Q =0.9683,which imply the good effect of the regression and prediction of the model.Third: As a comparison, the situation of symmetric triangular fuzzy number as the regression coefficients is calculated. The result shows that the model based on normal fuzzy number is superior to the model based on symmetric triangular fuzzy number.