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Statistical Methods for Fuzzy Data by Reinhard Viertl

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Chapter 20

a. First the fuzzy quantities x1*, x2*, y1*, and y2* have to be combined into a fuzzy vector with vector-characterizing function

Unnumbered Display Equation

Based on this fuzzy combined vector the estimatiors

Unnumbered Display Equation

are generalized to the fuzzy estimatiors 0* and 1* by applying the extension principle. For details compare the characterizing functions φj(·) in Remark 20.3 ad (d).

b. Here the fuzzy elements 0*, 1 *, and x* with corresponding membership functions have to be combined into a fuzzy 3-dimensional vector z*. Then the extension principle has to be applied to the function g(x) = θ0 + θ1 · x.

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