‎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.

‎One of the factors affecting the statistical analysis of the data is the presence of outliers‎. ‎The methods which are not affected by the outliers are called robust methods‎. ‎Robust regression methods are robust estimation methods of regression model parameters in the presence of outliers‎. ‎Besides outliers‎, ‎the linear dependency of regressor variables‎, ‎which is called multicollinearity‎, ‎the large number of regressor variables with respect to sample size‎, ‎specially in high dimensional sparse models‎, ‎are problems which result in efficiency reduction of inferences in classical regression methods‎. ‎In this paper‎, ‎we first study the disadvantages of classical least squares regression method‎, ‎when facing with outliers‎, ‎multicollinearity and sparse models‎. ‎Then‎, ‎we introduce and study robust and penalized regression methods‎, ‎as a solution to overcome these problems‎. ‎Furthermore‎, ‎considering outliers and multicollinearity or sparse models‎, ‎simultaneously‎, ‎we study penalized-robust regression methods‎. ‎We examine the performance of different estimators introdused in this paper‎, ‎through three different simulation studies‎. ‎A real data set is also analyzed using the proposed methods‎.