Multidimensional least-squares fitting with a fuzzy model

The aim of this paper is to deal with the question of fuzzy multivariable linear regression by least squares. Similar to the traditional least-squares method, we develop a fuzzy analogue by a distance defined on a fuzzy number space, and propose a fuzzy multivariable linear regression model. It is shown that the model has a unique solution and the solution can be given in an analytic expression. In this paper, we also give an index to evaluate the goodness of fit between the observed value and the estimated value.