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.


62J05 Linear regression; mixed models
62J99 Linear inference, regression
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