TITLE:
Robust Regression Analysis with LR-Type Fuzzy Input Variables and Fuzzy Output Variable
AUTHORS:
Dan Zhang, Qiujun Lu
KEYWORDS:
LR-Type Fuzzy Input Variables, LR-Type Fuzzy Output Variable, LMS-WLS, Outliers, Robust
JOURNAL NAME:
Journal of Data Analysis and Information Processing,
Vol.4 No.2,
May
19,
2016
ABSTRACT: 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.