Support vector fuzzy regression with fuzzy input-fuzzy output and fuzzy error

Abstract

In this paper, we investigate a new approach of fuzzy regression analysis based on support vectors when the available data and error variable are fuzzy quantities. In this approach, based on the concept of the distance between two parallel hyperplanes, we obtain the marginal hyperplanes and then, based on some constraints on the fuzzy data, we present an optimization problem to estimate the parameters of fuzzy regression model. The proposed method is investigated in two cases: with fuzzy fixed error and with fuzzy variable errors. To evaluate the proposed support vector fuzzy regression (SVFR) models, we present two indices of goodness of fit. Based on these indices, the presented SVFR models are compared with some other approaches on the numerical and simulated examples.