Fuzzy regression based on asymmetric support vector machines

Abstract

This paper presents a modified framework of support vector machines which is called asymmetric support vector machines (ASVMs) and is designed to evaluate the functional relationship for fuzzy linear and nonlinear regression models. In earlier works, in order to cope with different types of input–output patterns, strong assumptions were made regarding linear fuzzy regression models with symmetric and asymmetric triangular fuzzy coefficients. Excellent performance is achieved on some linear fuzzy regression models. However, the nonlinear fuzzy regression model has received relatively little attention, because such nonlinear fuzzy regression models having certain limitations. This study modifies the framework of support vector machines in order to overcome these limitations. The principle of ASVMs is applying an orthogonal vector into the weight vector in order to rotate the support hyperplanes. The prime merits of the proposed model are in its simplicity, understandability and effectiveness. Consequently, experimental results and comparisons are given to demonstrate that the basic idea underlying ASVMs can be effectively used for parameter estimation.