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Fuzzy regression analysis. (English) Zbl 0922.62058
Słowiński, Roman (ed.), Fuzzy sets in decision analysis, operations research and statistics. Boston: Kluwer Academic Publishers. Handb. Fuzzy Sets Ser. 1, 349-387 (1998).
Summary: Fuzzy regression analysis gives a fuzzy functional relationship between dependent and independent variables where vagueness is present in some form. The input data may be crisp or fuzzy. This chapter considers two types of fuzzy regression. The first is based on possibilistic concepts and the second upon a least squares approach. However, in both the notion of “best fit” incorporates the optimization of a functional associated with the problem. In possibilistic regression, this functional takes the form of a measure of the spreads of the estimated output, either as a weighted linear sum involving the estimated coefficients in linear regression, or as quadratic form in the case of exponential possibilistic regression. These optimization problems reduce to linear programming.
For the least squares approach, the functional to be minimized is an $$L_2$$ distance between the observed and estimated outputs. This reduces to a class of quadratic optimization problems and constrained quadratic optimization. The method that can incorporate stochastic fuzzy input and fuzzy kriging uses covariances to obtain BLUE estimators.
For the entire collection see [Zbl 0905.00031].

##### MSC:
 62J99 Linear inference, regression 62J05 Linear regression; mixed models