Fuzzy principal component regression (FPCR) for fuzzy input and output data

Abstract

Although fuzzy regression is widely employed to solve many problems in practice, what seems to be lacking is the problem of multicollinearity. In this paper, the fuzzy centers principal component analysis is proposed to first derive the fuzzy principal component scores. Then the fuzzy principal component regression (FPCR) is formed to overcome the problem of multicollinearity in the fuzzy regression model. In addition, a numerical example is used to demonstrate the proposed method and compare with other methods. On the basis of the results, we can conclude that the proposed method can provide a correct fuzzy regression model and avoid the problem of multicollinearity.