Abstract
This paper presents an approach which is useful for regression analysis in the case of heterogeneity of a set of observations, for which regression is evaluated. The proposed procedure consists of two stages. First, for a set of observations, fuzzy classification is determined. Due to this, homogenous classes of observations which are of hyperellipsoidal shape, are obtained. Then for each fuzzy class, the so called linear fuzzy regression is evaluated. In the paper the method of calculating linear fuzzy regression coefficients is given. It is a generalized version of the least squares method. The formula for the values of coefficients is given. Some properties of linear fuzzy regression are analyzed. It is proved that in one- and two-dimensional cases, the formulae are analogous to those for usual regression. A measure of goodness-of-fit and the method of determination of the number of fuzzy classes are also given. Presented examples indicate the superiority of fuzzy regression in comparison to usual regression in the case of heterogenous observations.
Published Version
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