Fuzzy Regression Model Dealing with Vague Possibility Grades and Its Characteristics

Abstract

Given that an interval-type fuzzy regression model illustrates the possibilities of an analysis target according to its intervals, its characteristics can be intuitively understood. Conversely, there is the important problem of properly describing the possibilities of an analysis target. In other words, a fuzzy regression model should be designed to illustrate an appropriate possibility interval according to data. We continue to propose models and approaches that illustrate the appropriate possibility intervals. These are models that correspond to samples that distort possibility intervals, maximize the sum of possibility grades obtained from an interval-type fuzzy regression model and so on. Thanks to various improvements, we obtained a model illustrating the appropriate possibility intervals. On the other hand, by using the possibilities of unusual samples, the centers of the model and the data distribution do not coincide and the possibility intervals might be distorted. For this reason, we assumed vagueness was included in the possibility grades as well as the proposed fuzzy regression model dealing with that vagueness. The proposed model can be obtained only by deciding the extent to which sample possibilities are considered. By verifying the model using a numerical example, the features were found. The appropriate possibility interval can be obtained by setting restrictions on the number of samples that are neglected during model construction. Then, by moderately increasing the magnitude of vagueness included in the possibility grades, we can manage distorted possibility intervals. This paper discusses the results obtained.