Fuzzy Robust Regression Analysis with Fuzzy Response Variable and Fuzzy Parameters Based on the Ranking of Fuzzy Sets

‎Robust regression is an appropriate alternative for ordinal regression when outliers exist in a given data set‎. ‎If we have fuzzy observations‎, ‎using ordinal regression methods can't model them; In this case‎, ‎using fuzzy regression is a good method‎. ‎When observations are fuzzy and there are outliers in the data sets‎, ‎using robust fuzzy regression methods are appropriate alternatives‎. ‎In this paper‎, ‎we propose a fuzzy least square regression analysis‎. ‎When independent variables are crisp‎, ‎the dependent variable is fuzzy number and outliers are present in the data set‎. ‎In the proposed method‎, ‎the residuals are ranked as the comparison of fuzzy sets‎. ‎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. ‎Weighted fuzzy least squares estimators (WFLSE) are obtained by using weight matrix‎. ‎Two examples are discussed and results of these examples are presented‎. ‎Finally‎, ‎we compare this proposed method with ordinal least squares method using the goodness of fit indices‎.