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‎In this paper a new weighted fuzzy ridge regression method for a given set of crisp input and triangular fuzzy output values is proposed‎. ‎In this regard‎, ‎ridge estimator of fuzzy parameters is obtained for regression model and its prediction error is calculated by using the weighted fuzzy norm of crisp ridge coefficients‎. . ‎To evaluate the proposed regression model‎, ‎we introduce the fuzzy coefficient of determination (FCD)‎. ‎Fuzzy regression is compared with its ridge version by using mean predict error and FCD‎, ‎numerically‎. ‎It is evident from comparison results the proposed fuzzy ridge regression is superior to the non-ridge counterpar

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‎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.

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In this paper, the difference between classical regression and fuzzy regression is discussed. In fuzzy regression, nonphase and fuzzy data can be used for modeling. While in classical regression only non-fuzzy data is used.
The purpose of the study is to investigate the possibility of regression method, least squares regression based on regression and linear least squares linear regression method based on fuzzy weight calculation for non-fuzzy input and fuzzy output using symmetric triangular fuzzy numbers. Further reliability, confidence intervals and fitness fit criterion is presented for choosing the optimal model.
Finally, by providing examples of the behavior of the proposed methods, the optimality of the regression hybrid model is shown by the least linear fuzzy squares.