Least-Squares Regression Based on Atanassov's Intuitionistic Fuzzy Inputs–Outputs and Atanassov's Intuitionistic Fuzzy Parameters

Based on the least-squares method, a new approach is proposed to the problem of regression modeling of imprecise quantities. In this approach, the available data, of both explanatory variable(s) and the response variable, as well as the parameters of the model, are assumed to be Atanassov´s intuitionistic fuzzy numbers. Therefore, the proposed model is a fully intuitionistic fuzzy model. Based on the similarity measure and the squared errors, two indices are proposed to investigate the goodness of fit of such models. Inside, using a real dataset, the application of the proposed approach in modeling some soil characteristics is studied. The predictive ability of the obtained model is evaluated by using the cross-validation method.