an:04186920
Zbl 0719.62086
B??rdossy, Andr??s
Note on fuzzy regression
EN
Fuzzy Sets Syst. 37, No. 1, 65-75 (1990).
00174412
1990
j
62J99 62J02 03E72 90C90
nonlinear programming; fuzzy regression; measures of vagueness
This note is strongly related to the Tanaka-approach to fuzzy regression [see, e.g., \textit{H. Tanaka} and \textit{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.
W.N??ther (Freiberg)
Zbl 0662.93066