Possibility Grades with Vagueness in Fuzzy Regression Models

The approach of fuzzy multivariate analysis models to handling errors in a sample is similar to that of statistical models. However, it is not assumed that a possibility grade may include vagueness. Possibility distribution is exhibited by an interval model by its intervals. When a possibility degree is defined by a triangular membership function, degrees are defined by the relationship between a sample and the model. Furthermore, the shape of a model is defined by samples. Therefore, it is natural to consider that vagueness is included in a possibility grade. In this study, assuming that vagueness is included in a possibility grade, we construct a fuzzy regression model to remove distortion from the data distribution. By controlling the vagueness of a grade using numerical examples generated by random numbers, it was possible to eliminate the distortion of models. In numerical examples, since the model was able to adjust vagueness, the result is reported. In addition to the obtained models, models obtained by changing samples to an outlier are considered.