Abstarct: In practical problems with non-exact component, the use of fuzzy sets eliminates some of the current restriction. Non-exact statistical analysis with non-precise (fuzzy) data has a widespread application in various fields of statistical sciences, such as quality control, regression and reliability. Regression analysis is a method to determine and analyze the relationship between statistical variables. In classical regression, it is assumed, variables and their corresponding observations, are crisp and there is no linear relationship among the predictor variables. However, they might not be correct. For example observations are non-exact or they might have reported non-precise. In such situations classical method cannot be used, instead we use the concept of fuzzy sets. In classical regression, if problem of multicollinearity exists, the result of least squares regression cannot be trusted. Many methods to deal with this problem are proposed, such as ridge regression, lasso regression, principal component regression and etc. In fuzzy regression, when the multicollinearity is present, the validity of model is reduced. In this regard, few studies have been done, that in this thesis we describe some of these methods and evaluate them. At the end, to extend the existing results, when the multicollinearity exists between the independent variables, for input and output fuzzy variables, we propose a new fuzzy ridge regression model. To check the existence of multicollinearity problem between the fuzzy predictor variables, we have defined a generalized variance inflation factor. In order to evaluate the goodness of fit, we have computed the mean squared prediction error and generalize coefficient of determination in simulation and real data examples.