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Note on fuzzy regression. (English) Zbl 0719.62086
This 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.

62J99 Linear inference, regression
62J02 General nonlinear regression
03E72 Theory of fuzzy sets, etc.
90C90 Applications of mathematical programming
Full Text: DOI
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