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Statistical Methods for Fuzzy Data by Reinhard Viertl

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18.3 Discrete state space

Let Θ = {θ1, …, θm} be discrete, and P a discrete probability distribution on Θ with point probabilities pj = Pj) for j = 1(1)m. Then the expected utility of a decision d for the fuzzy utility function U*(., d) is calculated using δ-level functions in the following way: The δ-cuts of the generalized expected utility PU*(, d),

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are calculated by

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and

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for all δ ∈ (0; 1].

The characterizing function χ(·) of PU*(, d) is obtained from the construction lemma:

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with C0[pU*(

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