Abstract: Possibilistic linear regression analysis for fuzzy data originated from a fuzzy phenomenon was Introduced by Tanaka et at.In this paper,four types of possibilistic linear regression model are proposed to develop Tanaka' s models which are called the Min problem,the Max problem and the Conjunction problem.The method for obtaining the parameters of the models consists of two steps,(1) determine the mean valuta of the parameters by using a linear least squares approach so that the merit of the models is to be able to fit fuzzy observed values more realistically; (2) compute the spreads of the parameters by a linear least squares approach or by reducing the problem to a conventional linear programming as treated by Tanaka's techniques while mean values are determined.The advantage of these models is that they can not only fit the main ideas of the data but also retain the advantages of fuzzy interval analysis.The exixtence of the models' s solution and mutual relations In these models are discussed.To Illustrate the approach for dealing with fuzzy data,two numerical examples are shown finally.