Fuzzy regression using asymmetric fuzzy coefficients and fuzzified neural networks

In this paper, first we explain several versions of fuzzy regression methods 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 triangular and trapezoidal fuzzy numbers. We show that the limitations of the fuzzy regression methods with the symmetric triangular fuzzy coefficients are remedied by such extension. Several formulations of linear programming problems are proposed for determining asymmetric fuzzy coefficients from numerical data. Finally, we show how fuzzified neural networks can be utilized as nonlinear fuzzy models in fuzzy regression. In the fuzzified neural networks, asymmetric fuzzy numbers are used as connection weights. The fuzzy connection weights of the fuzzified neural networks correspond to the fuzzy coefficients of the linear fuzzy models. Nonlinear fuzzy regression based on the fuzzified neural networks is illustrated by computer simulations where Type I and Type II membership functions are determined from numerical data.