Multiple Fuzzy Regression Model for Fuzzy Input-Output Data

A novel approach to the problem of regression modeling for fuzzy input-output data is introduced.
In order to estimate the parameters of the model, a distance on the space of interval-valued quantities is employed.
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.
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.
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.