Multiple Fuzzy Regression Model for Fuzzy Input-Output Data

Abstract

A novel approach to the problem of regression modeling for fuzzy input-output data is introduced.<br />In order to estimate the parameters of the model, a distance on the space of interval-valued quantities is employed.<br />By minimizing the sum of squared errors, a class of regression models is derived based on the interval-valued data obtained from the $alpha$-level sets of fuzzy input-output data.<br />Then, by integrating the obtained parameters of the interval-valued regression models, the optimal values of parameters for the main fuzzy regression model are estimated.<br />Numerical examples and comparison studies are given to clarify the proposed procedure, and to show the performance of the proposed procedure with respect to some common methods.