Constructing the linear regression models for the symbolic interval-values data using PSO algorithm

In the literature, some of methods are proposed for the symbolic interval-values data. They have the Centre method (CM), the MinMax method and the Centre and Range (CR) method. For the above methods, they needs solve the inverse of matrix. However, the dimension of this matrix is increased as increasing the variables. Moreover, the condition number of this matrix is large, it may cause a large error of solution (i.e. ill-conditioned). The above methods do not guarantee that the predicted values of the lower bounds will be lower than the predicted values of the upper bounds. To overcome the above problems, the particle swarm optimization (PSO) algorithm is applied to estimate the parameters of linear regression models. From the simulation results, the proposed method can provide satisfactory results.