Fuzzy regression analysis with non-symmetric fuzzy number coefficients and its neural network implementation

Abstract

Fuzzy regression analysis has usually been formulated using fuzzy linear models with symmetric triangular fuzzy number coefficients. In this paper, we first point out several drawbacks of such fuzzy linear models. Then we extend the fuzzy linear models to the case of nonsymmetric fuzzy number coefficients. We use nonsymmetric triangular fuzzy numbers and nonsymmetric trapezoidal fuzzy numbers as the coefficients of the fuzzy linear models. We propose three fuzzy regression methods for determining the nonsymmetric fuzzy number coefficients. Finally we suggest the use of fuzzified neural networks for nonlinear fuzzy regression analysis. In the fuzzified neural networks, connection weights are given as nonsymmetric fuzzy numbers. These fuzzy number connection weights correspond to the fuzzy number coefficients of the fuzzy linear models.