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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.

MSC:
62J99 Linear inference, regression
62J02 General nonlinear regression
03E72 Theory of fuzzy sets, etc.
90C90 Applications of mathematical programming
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[1] Abraham, T.P.; Ledolter, L., Statistical methods for forecasting, (1984), Wiley New York
[2] Dubois, D.; Prade, H., Fuzzy sets and systems. theory and applications, (1980), Academic Press New York · Zbl 0444.94049
[3] Heshmaty, B.; Kandel, A., Fuzzy linear regression and its applications to forecasting in uncertain environment, Fuzzy sets and systems, 15, 159-191, (1985) · Zbl 0566.62099
[4] Kandel, A., Fuzzy mathematical techniques with applications, (1986), Addison-Wesley Reading, MA
[5] Kandel, A.; Byatt, W.J., Fuzzy processes, Fuzzy sets and systems, 4, 117-152, (1980) · Zbl 0437.60002
[6] Kaufmann, A.; Gupta, M.M., Introduction to fuzzyarithmetic: theory and applications, (1985), Van Nostrand Reinhold New York
[7] Tanaka, H.; Uejima, S.; Asai, K., Linear regression analysis with fuzzy model, IEEE trans. systems man cybernet., 12, 903-907, (1982) · Zbl 0501.90060
[8] Zadeh, L.A., Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606
[9] Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning. part 3, Inform. sci., 9, 43-80, (1975) · Zbl 0404.68075
[10] Zimmermann, H.-J., Fuzzy set theory — and its applications, (1984), Kluwer Nijhoff Publishing Boston-Dordrecht
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