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Statistical Methods for Fuzzy Data by Reinhard Viertl

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Chapter 18

a. The classical situation is characterized by the indicator function IU(θ, d)(·) of U(θ, d) and a classical probability distribution P on Θ. Therefore the δ-level functions δ(· , d) and δ(· , d) are all identical and equal to U(· , d). The characterizing function of the generalized expected utility is the indicator function I PU(θ, d)(·).

b. If there exists a decision dB such that the support of the characterizing function of P*U*(, dB) has empty intersection with the supports of the characterizing functions χd(·) of the fuzzy expected utilities of all other decisions d, and the left end of supp[χdB(·)] is greater than all values in all supports of all other decisions, then dB is the uniquely determined Bayesian decision.

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