Fuzzy Robust Regressıon Analysıs Based On The Rankıng Of Fuzzy Sets

Abstract

Since fuzzy linear regression was introduced by Tanaka et al., fuzzy regression analysis has been widely studied and applied invarious areas. Diamond proposed the fuzzy least squares method to eliminate disadvantages in the Tanaka et al method. In this paper, we propose a modified fuzzy leasts quares regression analysis. When independent variables are crisp, the dependent variable is a fuzzy number and outliers are present in the dataset. In the proposed method, the residuals are ranked as the comparison of fuzzy sets, and the weight matrix is defined by the membership function of the residuals. To illustrate how the proposed method is applied, two examples are discussed and compared in methods from the literature. Results from the numerical examples using the proposed method give good solutions.