Fuzzy estimates of regression parameters in linear regression models for imprecise input and output data

The method for obtaining the fuzzy estimates of regression parameters with the help of “Resolution Identity” in fuzzy sets theory is proposed. The -level least-squares estimates can be obtained from the usual linear regression model by using the -level real-valued data of the corresponding fuzzy input and output data. The membership functions of fuzzy estimates of regression parameters will be constructed according to the form of “Resolution Identity” based on the -level least-squares estimates. In order to obtain the membership degree of any given value taken from the fuzzy estimate, optimization problems have to be solved. Two computational procedures are also provided to solve the optimization problems. c © 2002 Elsevier Science B.V. All rights reserved.