Linear fuzzy regression (Q1087276)

The author proposes the following regression procedure for analyzing heterogeneous data: Using a fuzzy clustering algorithm divide the data set into fuzzy clusters. Then for each cluster fit a linear model to the data by minimizing a weighted residual sum of squares. The weight of an observation is the membership grade of the observation for belonging to the pertinent cluster. These weights are obtained from the fuzzy clustering algorithm. The author also gives a method for determining the appropriate number of clusters. A different kind of fuzzy regression model is defined by \textit{H. Tanaka}, \textit{S. Uejima} and \textit{K. Asai} [IEEE Trans. Syst. Man Cybern. SMC-12, 903-907 (1982; Zbl 0501.90060)] and applied by \textit{B. Heshmaty} and \textit{A. Kandel} [Fuzzy Sets Syst. 15, 159-191 (1985; Zbl 0566.62099)].