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‎There are two main approches to the fuzzy regression (more precisely‎: ‎regression in fuzzy environment)‎: ‎the least of sum of distances (including two methods of least squared errors and least absolute errors) and the possibilistic method (the method of least whole vaguness under some restrictions)‎. ‎Beside‎, ‎some heuristic methods have been proposed to deal with fuzzy regression‎. ‎Some of them are based on a combination of two mentioned approaches‎. ‎Some of them are based on computational algorithmes‎. ‎A few of heuristic methods use the fuzzy inference systems‎. ‎Also‎, ‎there are some methods based on clustering‎, ‎artificial neural networks‎, ‎evolutionary algorithms‎, ‎and nonparametric procedures‎.

‎In this paper‎, ‎a history and basic ideas of the two main approaches to‎ ‎fuzzy regression are reveiwed‎, ‎and some heuristic methods in this topic are investigated‎. ‎Moreover‎, ‎10 criterion are proposed by which one can‎ ‎evaluate and compare fuzzy regression models‎.

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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.