Author(s)

Dan Zhang, Qiujun Lu

College of Science, University of Shanghai for Science and Technology, Shanghai, China.

In this paper, we propose a fuzzy linear regression model with LR-type fuzzy input variables and fuzzy output variable, the fuzzy extent of which may be different. Then we give the iterative solution of the proposed model based on the Weighted Least Squares estimation procedure. Some properties of the estimates are proved. We also define suitable goodness of fit index and its adjusted version useful to evaluate the performances of the proposed model. Based on the Least Median Squares-Weighted Least Squares (LMS-WLS) estimation procedure, we give robust estimation steps for the proposed model. Compared with the well-known fuzzy Least Squares method, the effectiveness of our model on reducing the outliers influence is shown by using two examples.

LR-Type Fuzzy Input Variables, LR-Type Fuzzy Output Variable, LMS-WLS, Outliers, Robust

Zhang, D. and Lu, Q. (2016) Robust Regression Analysis with LR-Type Fuzzy Input Variables and Fuzzy Output Variable. Journal of Data Analysis and Information Processing, 4, 64-80. doi: 10.4236/jdaip.2016.42006.