Note on fuzzy regression.

*(English)*Zbl 0719.62086This note is strongly related to the Tanaka-approach to fuzzy regression [see, e.g., H. Tanaka and J. Watada, Fuzzy sets Syst. 27, No.3, 275-289 (1988; Zbl 0662.93066)]. The problem is to find a fuzzy regression function f(x,a) generated by a fuzzy parameter a which covers, on the one hand, all fuzzy data \(y_ 1,...,y_ T\) at least to a given degree h and the vagueness of which is, on the other hand, as small as possible. Whereas Tanaka et al. have considered linear regression and a special vagueness criterion, the author formulates this problem for nonlinear setups and several measures of vagueness.

Under several additional assumptions on f(x,a) (continuity, monotonicity, linearity) he finds the associated programming problems which simplify to linear ones in the case of linear regression. Two numerical examples are given.

Under several additional assumptions on f(x,a) (continuity, monotonicity, linearity) he finds the associated programming problems which simplify to linear ones in the case of linear regression. Two numerical examples are given.

Reviewer: W.Näther (Freiberg)

##### MSC:

62J99 | Linear inference, regression |

62J02 | General nonlinear regression |

03E72 | Theory of fuzzy sets, etc. |

90C90 | Applications of mathematical programming |

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