Fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks

In this paper, first we explain several versions of fuzzy regression method s based on linear fuzzy models with symmetric triangular fuzzy coefficients . Next we point out some limitations of such fuzzy regression methods. Then we extend the symmetric triangular fuzzy coefficients to asymmetric triang ular and trapezoidal Fuzzy numbers. We show that the limitations of the fuz zy regression methods with the symmetric triangular fuzzy coefficients are remedied by such extension. Several formulations of linear programming prob lems are proposed for determining asymmetric fuzzy coefficients from numeri cal data. Finally, we show how fuzzified neural networks can be utilized as nonlinear fuzzy models in fuzzy regression. In the fuzzified neural networ ks, asymmetric fuzzy numbers are used as connection weights. The fuzzy conn ection weights of the fuzzified neural networks correspond to the fuzzy coe fficients of the linear fuzzy models. Nonlinear fuzzy regression based on t he fuzzified neural networks is illustrated by computer simulations where T ype I and Type II membership functions are determined from numerical data. (C) 2001 Elsevier Science B.V. All rights reserved.