Linear regression analysis for fuzzy input and output data using the extension principle

The method for obtaining the fuzzy least squares estimators with the help of the extension principle in fuzzy sets theory is proposed. The membership functions of fuzzy least squares estimators will be constructed according to the usual least squares estimators. In order to obtain the membership value of any given value taken from the fuzzy least squares estimator, optimization problems have to be solved. We also provide the methodology for evaluating the predicted fuzzy output from the given fuzzy input data.