Linear regression with random fuzzy variables: Extended classical estimates, best linear estimates, least squares estimates.(English)Zbl 0930.62072

Summary: This paper deals with problems which arise if for well justified statistical models like linear regression only fuzzy data are available. Three approaches are discussed: The first one is an application of Zadeh’s extension principle to optimal classical estimators. Here, the result is that they, in general, do not keep their optimality properties. The second one is the attempt to develop a certain kind of linear theory for fuzzy random variables w.r.t. extended addition and scalar multiplication. The main problem in this connection is that fuzzy sets, with these extended operations, do not constitute a linear space. Therefore, in the third approach, the least squares approximation principle for fuzzy data is investigated, which leads to most acceptable results.

MSC:

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

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