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Linear regression with random fuzzy observations. (English) Zbl 0714.62063

Summary: The aim of the paper is to develop a linear estimation theory for the parameter in a linear regression model if random fuzzy-set-valued observations are available. Therefore fuzzy sets and their basic (linear) operations and random fuzzy sets, especially their expectation and variance, are introduced and applied to random fuzzy numbers which are used to model vague observations. For a well-defined linear regression model the BLUE is characterized which only in special cases coincides approximately with the so-called extended least squares estimator.

MSC:

62J05 Linear regression; mixed models
62J99 Linear inference, regression
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[1] DOI: 10.1016/0022-247X(65)90049-1 · Zbl 0163.06301
[2] DOI: 10.1016/S0165-0114(85)80004-X · Zbl 0582.62066
[3] Bandemer , H. 1988.Fuzzy analogues to partial-least-squares techniques in multivariate data analysis, 62–77. Freiberger Forschungsheft D: H. BANDEMER.
[4] Dubois D., Fuzzy Sets and Systems; Theory and Applications (1980) · Zbl 0444.94049
[5] Fbechet M., Ann. Frist, II, Poincare 10 pp 215– (1948)
[6] DOI: 10.1016/0022-247X(87)90277-0 · Zbl 0617.60013
[7] Kbuse R., Reidel Publ. Comp., Dordrecht 122 (1987)
[8] Kwaeerkaak H., Inf Sci 15 pp 1– (1978) · Zbl 0438.60004
[9] Matheron G., Random Sets and Integral Geometry (1975) · Zbl 0321.60009
[10] DOI: 10.1016/0022-247X(86)90093-4 · Zbl 0592.60004
[11] Stoyan D., Stochastic Geometry audits Applications (1987)
[12] Stoyan , D. 1989.On means medians and variances of random compact sets, 99–104. BERLIN: A. HUBLER, W.NAGEL, B.D. RIPLEY, G. WERNER.
[13] DOI: 10.1016/S0019-9958(65)90241-X · Zbl 0139.24606
[14] Ziezold , E.L. 1989.On expected figures in the plane. In: Geobild, 105–110. Berlin: A. HUBLEB, W. NAGEL, B. D. RIPLEY, G. WEBNEB. · Zbl 0696.60018
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